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Journal articles on the topic 'Integral identities'

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Published: 10 March 2023

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1

Ansari, Alireza, and Mohammad Rasool Masomi. "Some integral identities for products of Airy functions using integral transforms." Asian-European Journal of Mathematics 11, no. 03 (May 3, 2018): 1850046. http://dx.doi.org/10.1142/s1793557118500468.

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In this paper, using the integral identities of Bessel functions, we obtain new integral identities for the products of Airy functions. We get various integrals involving the Widder potential, the Fourier sine and cosine transforms of the products of Airy functions in terms of some special functions.

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2

Sarikaya, Mehmet Zeki, and Hasan Ogunmez. "On New Inequalities via Riemann-Liouville Fractional Integration." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/428983.

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We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities. Finally, we develop some integral inequalities for the fractional integral using differentiable convex functions.

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3

Yürekli, O. "Identities on fractional integrals and various integral transforms." Applied Mathematics and Computation 187, no. 1 (April 2007): 559–66. http://dx.doi.org/10.1016/j.amc.2006.09.001.

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4

Zlobin, S. A. "On some integral identities." Russian Mathematical Surveys 57, no. 3 (June 30, 2002): 617–18. http://dx.doi.org/10.1070/rm2002v057n03abeh000520.

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5

Bernstein, Dennis S. "Some Matrix Integral Identities." SIAM Review 38, no. 1 (March 1996): 147–48. http://dx.doi.org/10.1137/1038012.

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6

Wu, Xia, JinRong Wang, and and Jialu Zhang. "Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel." Mathematics 7, no. 9 (September 12, 2019): 845. http://dx.doi.org/10.3390/math7090845.

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In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving left-sided and right-sided fractional integrals with exponential kernels for convex functions. Finally, some applications to special means of real number are presented.

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7

Rockower, Edward B. "Integral Identities for Random Variables." American Statistician 42, no. 1 (February 1988): 68. http://dx.doi.org/10.2307/2685265.

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8

Rockower, Edward B. "Integral Identities for Random Variables." American Statistician 42, no. 1 (February 1988): 68–72. http://dx.doi.org/10.1080/00031305.1988.10475526.

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9

Crouch, P. E., and F. Lamnabhi-Lagarrigue. "Algebraic and multiple integral identities." Acta Applicandae Mathematicae 15, no. 3 (June 1989): 235–74. http://dx.doi.org/10.1007/bf00047532.

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10

Kumar, Hemant, and R. C. Singh Chandel. "RELATIONS AND IDENTITIES VIA CONTOUR INTEGRAL REPRESENTATIONS INVOLVING HURWITZ-LERCH ZETA TYPE FUNCTIONS FOR TWO VARIABLE SRIVASATAVA-DAOUST FUNCTIONS." Jnanabha 51, no. 01 (2021): 125–32. http://dx.doi.org/10.58250/jnanabha.2021.51117.

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In this paper, we derive certain relations of the series of two variable Srivastava-Daoust functions with some known Mittag- Leffler and hypergeometric functions of two variables. Again, by these functions we obtain certain identities with other integral representations also. Finally, on application of these contour integral formulae of respective Srivastava-Daoust functions, we determine certain identities of the integrals involving the Hurwitz-Lerch zeta type functions.

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11

Pareek, Neelu, and Arvind Gupta. "ON SOLUTION OF FRACTIONAL ADVECTION -DISPERSION EQUATION USING NHPM." Jnanabha 51, no. 01 (2021): 133–41. http://dx.doi.org/10.58250/jnanabha.2021.51118.

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In this paper, we derive certain relations of the series of two variable Srivastava-Daoust functions with some known Mittag- Leffler and hypergeometric functions of two variables. Again, by these functions we obtain certain identities with other integral representations also. Finally, on application of these contour integral formulae of respective Srivastava-Daoust functions, we determine certain identities of the integrals involving the Hurwitch-Lerch zeta type functions.

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12

Zeki Sarikaya, Mehmet. "On the Generalized Weighted Integral Inequality for Double Integrals." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (January 1, 2015): 169–79. http://dx.doi.org/10.2478/aicu-2014-0008.

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Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

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13

Kim, Dae San, Dmitry V. Dolgy, Hyun-Mee Kim, Sang-Hun Lee, and Taekyun Kim. "Integral Formulae of Bernoulli Polynomials." Discrete Dynamics in Nature and Society 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/269847.

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Recently, some interesting and new identities are introduced in (Hwang et al., Communicated). From these identities, we derive some new and interesting integral formulae for the Bernoulli polynomials.

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14

Apelblat, Alexander, and Francesco Mainardi. "Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)." Symmetry 13, no. 2 (February 22, 2021): 354. http://dx.doi.org/10.3390/sym13020354.

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Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

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15

Sofo, Anthony. "Triple integral identities and zeta functions." Applicable Analysis and Discrete Mathematics 4, no. 2 (2010): 347–60. http://dx.doi.org/10.2298/aadm100515025s.

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Some new identities are given for the representation of binomial sums. A master theorem is developed from which integral and closed form results, in terms of Zeta functions and harmonic numbers, are developed for sums of the type ?n?1 tn/n4(an+j/j)(bn+k/k)(cn+l/l).

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16

Bhuvan, E. N. "On Ramanujan’s Incomplete Elliptic Integral Identities." Indian Journal of Pure and Applied Mathematics 51, no. 4 (December 2020): 1737–51. http://dx.doi.org/10.1007/s13226-020-0493-6.

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17

Kilar, Neslihan, and Yilmaz Simsek. "Formulas involving sums of powers, special numbers and polynomials arising from p-adic integrals, trigonometric and generating functions." Publications de l'Institut Math?matique (Belgrade) 108, no. 122 (2020): 103–20. http://dx.doi.org/10.2298/pim2022103k.

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The formula for the sums of powers of positive integers, given by Faulhaber in 1631, is proven by using trigonometric identities and some properties of the Bernoulli polynomials. Using trigonometric functions identities and generating functions for some well-known special numbers and polynomials, many novel formulas and relations including alternating sums of powers of positive integers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the Fubini numbers, the Stirling numbers, the tangent numbers are also given. Moreover, by applying the Riemann integral and p-adic integrals involving the fermionic p-adic integral and the Volkenborn integral, some new identities and combinatorial sums related to the aforementioned numbers and polynomials are derived. Furthermore, we serve up some revealing and historical remarks and observations on the results of this paper.

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18

SUZUKI, MASUO. "CORRELATION IDENTITIES AND APPLICATION." International Journal of Modern Physics B 16, no. 13 (May 30, 2002): 1749–65. http://dx.doi.org/10.1142/s0217979202011172.

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General correlation identities are derived in a unified way using the quantum analysis,1–4 which include the well-known classical correlation identities5–7 such as the Ising correlation identities.5,6 In particular, quantum correlation identities are applied to the Heisenberg models and the transverse Ising model with local constants of motion. Integral identities are also presented in the spirit of the Gauss–Manin connection and they are applied to derive the generalized Bernoulli equation on the pressure and energy of ideal quantum gasses. There are many applications to condensed matter physics, which will be summarized in the present article together with an integrated list of papers on such applications in order to show how useful these correlation identities are.

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19

Wang, Hua, Jamroz Khan, Muhammad Adil Khan, Sadia Khalid, and Rewayat Khan. "The Hermite–Hadamard–Jensen–Mercer Type Inequalities for Riemann–Liouville Fractional Integral." Journal of Mathematics 2021 (May 13, 2021): 1–18. http://dx.doi.org/10.1155/2021/5516987.

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In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer type for Riemann–Liouville fractional integrals. We prove integral identities, and with the help of these identities and some other eminent inequalities, such as Jensen, Hölder, and power mean inequalities, we obtain bounds for the difference of the newly obtained inequalities.

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20

Farid, Ghulam, Hafsa Yasmeen, Chahn Yong Jung, Soo Hak Shim, and Gaofan Ha. "Refinements and Generalizations of Some Fractional Integral Inequalities via Strongly Convex Functions." Mathematical Problems in Engineering 2021 (March 27, 2021): 1–18. http://dx.doi.org/10.1155/2021/6667226.

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In this article, we have established the Hadamard inequalities for strongly convex functions using generalized Riemann–Liouville fractional integrals. The findings of this paper provide refinements of some fractional integral inequalities. Furthermore, the error bounds of these inequalities are given by using two generalized integral identities.

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21

Haddad, Roudy El. "Repeated integration and explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m'}\)." Open Journal of Mathematical Sciences 6, no. 1 (June 10, 2022): 51–75. http://dx.doi.org/10.30538/oms2022.0178.

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Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for both the definite as well as indefinite form. These reduction formulae express these repetitive integrals in terms of single integrals. We also derive a generalization of the fundamental theorem of calculus that expresses a definite integral in terms of an indefinite integral for repeated and recurrent integrals. From the recurrent integral formulae, we derive some partition identities. Then we provide an explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m'}\) in terms of a shifted multiple harmonic star sum. Additionally, we use this integral to derive new expressions for the harmonic sum and repeated harmonic sum.

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22

GULSHAN, GHAZALA, RASHIDA HUSSAIN, and ASGHAR ALI. "INVESTIGATION OF SOME RESULTS ARISING FROM POST QUANTUM CALCULUS." Journal of Science and Arts 20, no. 3 (September 30, 2020): 561–72. http://dx.doi.org/10.46939/j.sci.arts-20.3-a06.

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This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and (p,q)-integrals. The purpose of this paper is to establish different type of identities for (p,q)-calculus. Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.

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23

Kim, Dae San. "Identities of Symmetry for Generalized Euler Polynomials." International Journal of Combinatorics 2011 (April 11, 2011): 1–12. http://dx.doi.org/10.1155/2011/432738.

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We derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the -adic fermionic integral expression of the generating function for the generalized Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized power sums.

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24

Rim, Seog-Hoon, Joung-Hee Jin, and Joohee Jeong. "Integral Formulae of Bernoulli and Genocchi Polynomials." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/472010.

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Recently, some interesting and new identities are introduced in the work of Kim et al. (2012). From these identities, we derive some new and interesting integral formulae for Bernoulli and Genocchi polynomials.

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25

Luo, Minjie, Minghui Xu, and Ravinder Krishna Raina. "On Certain Integrals Related to Saran’s Hypergeometric Function FK." Fractal and Fractional 6, no. 3 (March 13, 2022): 155. http://dx.doi.org/10.3390/fractalfract6030155.

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In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function FK, which has applications in specific branches of applied physics and statistics (see below). We employ methods based on the k-dimensional fractional integration by parts to obtain our main integral identities. The first integral generalizes Koschmieder’s result and the second integral extends one of Erdélyi’s classical hypergeometric integral. Some useful special cases and important remarks are also discussed.

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26

Awan, Muhammad Uzair, Sadia Talib, Yu-Ming Chu, Muhammad Aslam Noor, and Khalida Inayat Noor. "Some New Refinements of Hermite–Hadamard-Type Inequalities Involving ψk-Riemann–Liouville Fractional Integrals and Applications." Mathematical Problems in Engineering 2020 (April 25, 2020): 1–10. http://dx.doi.org/10.1155/2020/3051920.

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The main objective of this article is to establish some new fractional refinements of Hermite–Hadamard-type inequalities essentially using new ψk-Riemann–Liouville fractional integrals, where k>0. Using this new fractional integral, we also derive two new fractional integral identities. Applications of the obtained results are also discussed.

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27

Vivas-Cortez, Miguel, Muhammad Uzair Awan, Sehrish Rafique, Muhammad Zakria Javed, and Artion Kashuri. "Some novel inequalities involving Atangana-Baleanu fractional integral operators and applications." AIMS Mathematics 7, no. 7 (2022): 12203–26. http://dx.doi.org/10.3934/math.2022678.

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<abstract><p>As we know, Atangana and Baleanu developed great fractional integral operators which used the generalized Mittag-Leffler function as non-local and non-singular kernel. Inspired by these integral operators, we derive in this paper two new fractional integral identities involving Atangana-Baleanu fractional integrals. Using these identities as auxiliary results, we establish new fractional counterparts of classical inequalities essentially using first and second order differentiable higher order strongly $ n $-polynomial convex functions. We also discuss several important special cases of the main results. In order to show the efficiency of our main results, we offer applications for special means and for differentiable functions of first and second order that are in absolute value bounded.</p></abstract>

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28

Liu, Chiu-Chu Melissa, Kefeng Liu, and Jian Zhou. "Mariño-Vafa formula and Hodge integral identities." Journal of Algebraic Geometry 15, no. 2 (May 1, 2006): 379–98. http://dx.doi.org/10.1090/s1056-3911-05-00419-4.

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29

Liu, Hongmei, and Tianming Wang. "Elimination and Identities with the Integral Sign." Journal of Systems Science and Complexity 19, no. 4 (December 2006): 470–77. http://dx.doi.org/10.1007/s11424-006-0470-0.

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30

Chang, Shu-Chiuan, and Wenya Wang. "Spanning trees on lattices and integral identities." Journal of Physics A: Mathematical and General 39, no. 33 (August 2, 2006): 10263–75. http://dx.doi.org/10.1088/0305-4470/39/33/001.

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31

Luangboon, Waewta, Kamsing Nonlaopon, Jessada Tariboon, and Sotiris K. Ntouyas. "Simpson- and Newton-Type Inequalities for Convex Functions via (p,q)-Calculus." Mathematics 9, no. 12 (June 9, 2021): 1338. http://dx.doi.org/10.3390/math9121338.

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In this paper, we establish several new (p,q)-integral identities involving (p,q)-integrals by using the definition of a (p,q)-derivative. These results are then used to derive (p,q)-integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.

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32

Sofo, Anthony, and Amrik Singh Nimbran. "Euler Sums and Integral Connections." Mathematics 7, no. 9 (September 9, 2019): 833. http://dx.doi.org/10.3390/math7090833.

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In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler’s work on the subject followed by notations used in the body of the paper. After discussing some alternating Euler sums, we investigate the connection of integrals of inverse trigonometric and hyperbolic type functions to generate many new Euler sum identities. We also give some new identities for Catalan’s constant, Apery’s constant and a fast converging identity for the famous ζ ( 2 ) constant.

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33

Chasreechai, Saowaluck, Muhammad Aamir Ali, Muhammad Amir Ashraf, Thanin Sitthiwirattham, Sina Etemad, Manuel De la Sen, and Shahram Rezapour. "On New Estimates of q-Hermite–Hadamard Inequalities with Applications in Quantum Calculus." Axioms 12, no. 1 (January 2, 2023): 49. http://dx.doi.org/10.3390/axioms12010049.

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In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities.

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34

Li, Yixia, Muhammad Samraiz, Ayesha Gul, Miguel Vivas-Cortez, and Gauhar Rahman. "Hermite-Hadamard Fractional Integral Inequalities via Abel-Gontscharoff Green’s Function." Fractal and Fractional 6, no. 3 (February 23, 2022): 126. http://dx.doi.org/10.3390/fractalfract6030126.

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The Hermite-Hadamard inequalities for κ-Riemann-Liouville fractional integrals (R-LFI) are presented in this study using a relatively novel approach based on Abel-Gontscharoff Green’s function. In this new technique, we first established some integral identities. Such identities are used to obtain new results for monotonic functions whose second derivative is convex (concave) in absolute value. Some previously published inequalities are obtained as special cases of our main results. Various applications of our main consequences are also explored to special means and trapezoid-type formulae.

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35

Kim, Dae San. "IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY." Annals of the Alexandru Ioan Cuza University - Mathematics 60, no. 1 (January 1, 2014): 19–36. http://dx.doi.org/10.2478/aicu-2013-0006.

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Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

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36

Aylikci, Fatih, Nese Dernek, and Gulesin Balaban. "New identities on some generalized integral transforms and their applications." Filomat 36, no. 9 (2022): 2947–60. http://dx.doi.org/10.2298/fil2209947a.

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In this paper the authors gave an iteration identity for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Using this identity a Parseval-Goldstein type theorem for the L2n-transform and the G2n-transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given.

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37

Kalsoom, Humaira, Miguel Vivas-Cortez, and Muhammad Amer Latif. "Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus." Entropy 23, no. 10 (September 22, 2021): 1238. http://dx.doi.org/10.3390/e23101238.

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In this paper, we establish new (p,q)κ1-integral and (p,q)κ2-integral identities. By employing these new identities, we establish new (p,q)κ1 and (p,q)κ2- trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results.

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38

Kim, D. S., T. Kim, J. Choi, and Y. H. Kim. "Some Identities on Bernoulli and Euler Numbers." Discrete Dynamics in Nature and Society 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/486158.

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Recently, Kim introduced the fermionicp-adic integral onZp. By using the equations of the fermionic and bosonicp-adic integral onZp, we give some interesting identities on Bernoulli and Euler numbers.

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39

Buss, Adam C. "Construction of Generalized Integral Formulas by Means of Laplace Transformations." IU Journal of Undergraduate Research 2, no. 1 (May 31, 2016): 36–40. http://dx.doi.org/10.14434/iujur.v2i1.20922.

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We present a method for the construction of integral identities that contain an undetermined function. Except for mild restrictions, this function can be chosen arbitrarily. Our method is illustrated by several examples leading to new integral identities.

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40

Semenov, Vladimir I. "Special Properties of Plane Solenoidal Fields." Mathematics 9, no. 16 (August 6, 2021): 1863. http://dx.doi.org/10.3390/math9161863.

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Algebraic and integral identities have been obtained for a pair or a triple of plane solenoidal fields. We obtain sufficient potentiality conditions for a plane vector field. The integral identities are also important for exact a priori estimates.

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41

Farid, Ghulam, Hafsa Yasmeen, Hijaz Ahmad, and Chahn Yong Jung. "Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly $ (\alpha, m) $-convex functions." AIMS Mathematics 6, no. 10 (2021): 11403–24. http://dx.doi.org/10.3934/math.2021661.

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<abstract><p>In this paper Hadamard type inequalities for strongly $ (\alpha, m) $-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly $ m $-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.</p></abstract>

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42

Bushell, P. J., and W. Okrasiński. "Nonlinear Volterra Integral Equations and the Apéry Identities." Bulletin of the London Mathematical Society 24, no. 5 (September 1992): 478–84. http://dx.doi.org/10.1112/blms/24.5.478.

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43

Wilf, Herbert S., and Doron Zeilberger. "Rational Function Certification\\ Of Multisum/integral/``$q$'' Identities." Bulletin of the American Mathematical Society 27, no. 1 (July 1, 1992): 148–54. http://dx.doi.org/10.1090/s0273-0979-1992-00297-5.

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44

Norris, Andrew N. "Integral identities for reflection, transmission, and scattering coefficients." Journal of the Acoustical Society of America 144, no. 4 (October 2018): 2109–15. http://dx.doi.org/10.1121/1.5058681.

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45

Lei, Guang-Tsai. "Characterization of Electromagnetic Cavity Resonators by Integral Identities." SIAM Journal on Mathematical Analysis 42, no. 2 (January 2010): 634–45. http://dx.doi.org/10.1137/090751645.

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46

Dokuchaev, Michael A., and Jairo Z. Gonçalves. "Semigroup identities on units of integral group rings." Glasgow Mathematical Journal 39, no. 1 (January 1997): 1–6. http://dx.doi.org/10.1017/s0017089500031839.

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AbstractLet U(RG) be the group of units of a group ring RG over a commutative ring R with 1. We say that a group is an SIT-group if it is an extension of a group which satisfies a semigroup identity by a torsion group. It is a consequence of the main result that if G is torsion and R = Z, then U(RG) is an SIT-group if and only if G is either abelian or a Hamiltonian 2-group. If R is a local ring of characteristic 0 only the first alternative can occur.

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47

Ansari, Alireza, and Amirhossein Refahi Sheikhani. "New identities for the Wright and the Mittag-Leffler functions using the Laplace transform." Asian-European Journal of Mathematics 07, no. 03 (September 2014): 1450038. http://dx.doi.org/10.1142/s1793557114500387.

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In this paper, we state three theorems for the inverse Laplace transform and using these theorems we obtain new integral identities involving the products of the Wright and Mittag-Leffler functions. The relationships of these integral identities with the Stieltjes transform are also given.

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48

Vivas-Cortez, Miguel, Muhammad Uzair Awan, Muhammad Zakria Javed, Artion Kashuri, Muhammad Aslam Noor, and Khalida Inayat Noor. "Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications." AIMS Mathematics 7, no. 2 (2021): 3203–20. http://dx.doi.org/10.3934/math.2022177.

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<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

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Zhang, Zhi, JinRong Wang, and JianHua Deng. "Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/136035.

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By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.

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50

Jang, Lee-Chae. "On Multiple Generalizedw-Genocchi Polynomials and Their Applications." Mathematical Problems in Engineering 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/316870.

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We define the multiple generalizedw-Genocchi polynomials. By using fermionicp-adic invariant integrals, we derive some identities on these generalizedw-Genocchi polynomials, for example, fermionicp-adic integral representation, Witt's type formula, explicit formula, multiplication formula, and recurrence formula for thesew-Genocchi polynomials.

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