Relevant bibliographies by topics / Geometric-analytic inequalities

Academic literature on the topic 'Geometric-analytic inequalities'

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Published: 10 March 2023

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Journal articles on the topic "Geometric-analytic inequalities"

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Ku, Hsu-Tung, Mei-Chin Ku, and Xin-Min Zhang. "Analytic and geometric isoperimetric inequalities." Journal of Geometry 53, no. 1-2 (July 1995): 100–121. http://dx.doi.org/10.1007/bf01224044.

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Brooks, Robert. "Book Review: Isoperimetric inequalities: Differential geometric and analytic perspectives." Bulletin of the American Mathematical Society 39, no. 04 (July 10, 2002): 581–85. http://dx.doi.org/10.1090/s0273-0979-02-00954-0.

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Venkateswarlu, Bolenini, Pinninti Thirupathi Reddy, Şahsene Altınkaya, Nattakan Boonsatit, Porpattama Hammachukiattikul, and Vaishnavy Sujatha. "On a Certain Subclass of Analytic Functions Defined by Touchard Polynomials." Symmetry 14, no. 4 (April 18, 2022): 838. http://dx.doi.org/10.3390/sym14040838.

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This paper focuses on the establishment of a new subfamily of analytic functions including Touchard polynomials. Then, we attempt to obtain geometric properties such as coefficient inequalities, distortion properties, extreme points, radii of starlikeness and convexity, partial sums, neighbourhood results and integral means’ inequality for this class. The symmetry properties of the subfamily of functions established in the current paper may be examined as future research directions.
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Al-shbeil, Isra, Jianhua Gong, and Timilehin Gideon Shaba. "Coefficients Inequalities for the Bi-Univalent Functions Related to q-Babalola Convolution Operator." Fractal and Fractional 7, no. 2 (February 4, 2023): 155. http://dx.doi.org/10.3390/fractalfract7020155.

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This article defines a new operator called the q-Babalola convolution operator by using quantum calculus and the convolution of normalized analytic functions in the open unit disk. We then study a new class of analytic and bi-univalent functions defined in the open unit disk associated with the q-Babalola convolution operator. The main results of the investigation include some upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szego inequalities for the functions in the new class. Many applications of the finds are highlighted in the corollaries based on the various unique choices of the parameters, improving the existing results in Geometric Function Theory.
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Ibrahim, Rabha W., Rafida M. Elobaid, and Suzan J. Obaiys. "Geometric Inequalities via a Symmetric Differential Operator Defined by Quantum Calculus in the Open Unit Disk." Journal of Function Spaces 2020 (August 18, 2020): 1–8. http://dx.doi.org/10.1155/2020/6932739.

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The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q-differential operator defining new classes of analytic functions. We study the geometric representations with applications. The applications deliberated to indicate the certainty of resolutions of a category of symmetric differential equations type Briot-Bouquet.
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Singh, Gagandeep, and Gurcharanjit Singh. "COEFFICIENT PROBLEMS FOR THE SUBCLASSES OF SAKAGUCHI TYPE FUNCTIONS ASSOCIATED WITH SINE FUNCTION." Jnanabha 51, no. 02 (2021): 237–43. http://dx.doi.org/10.58250/jnanabha.2021.51230.

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Abstract The estimation of the upper bound for certain coefficient relations of various subclasses of analytic functions is an active topic of research in Geometric function theory. In this paper, certain subclasses of Sakaguchi type functions are defined by subordinating to sine function in the open unit disc E = {z : |z| < 1} and some coefficient inequalities such as Fekete-Szegö inequality, Second Hankel determinant, Zalcman functional and third Hankel determinant are investigated.
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Aldawish, Ibtisam, Rabha W. Ibrahim, and Suzan J. Obaiys. "A Class of Symmetric Fractional Differential Operator Formed by Special Functions." Journal of Mathematics 2022 (August 2, 2022): 1–10. http://dx.doi.org/10.1155/2022/8339837.

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In light of a certain sort of fractional calculus, a generalized symmetric fractional differential operator based on Raina’s function is built. The generalized operator is then used to create a formula for analytic functions of type normalized. We use the ideas of subordination and superordination to show a collection of inequalities using the suggested differential operator. The new Raina’s operator is also used to the generalized kinematic solutions (GKS). Using the concepts of subordination and superordination, we provide analytic solutions for GKS. As a consequence, a certain hypergeometric function provides the answer. A fractional coefficient differential operator is also created. The geometric and analytic properties of the object are being addressed. The symmetric differential operator in a complex domain is shown to be a generalized fractional differential operator. Finally, we explore the characteristics of the Raina’s symmetric differential operator.
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SONG, ZHIGANG, J. Q. LIANG, and L. F. WEI. "SPIN-PARITY EFFECT IN VIOLATION OF BELL'S INEQUALITIES." Modern Physics Letters B 28, no. 01 (December 23, 2013): 1450004. http://dx.doi.org/10.1142/s0217984914500043.

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Analytic formulas of Bell correlations are derived in terms of quantum probability statistics under the assumption of measuring outcome-independence and the Bell's inequalities (BIs) are extended to general bipartite-entanglement macroscopic quantum-states (MQS) of arbitrary spins. For a spin-½ entangled state we find analytically that the violations of BIs really resulted from the quantum nonlocal correlations. However, the BIs are always satisfied for the spin-1 entangled MQS. More generally the quantum nonlocality does not lead to the violation for the integer spins since the nonlocal interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spins due to the nontrivial Berry phase, and thus the violation of BIs is understood remarkably as an effect of geometric phase. Specifically, our generic observation of the spin-parity effect can be experimentally tested with the entangled photon-pairs.
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Aldawish, Ibtisam, and Rabha W. Ibrahim. "Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions." Fractal and Fractional 5, no. 4 (November 17, 2021): 228. http://dx.doi.org/10.3390/fractalfract5040228.

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The current study acts on the notion of quantum calculus together with a symmetric differential operator joining a special class of meromorphic multivalent functions in the puncher unit disk. We formulate a quantum symmetric differential operator and employ it to investigate the geometric properties of a class of meromorphic multivalent functions. We illustrate a set of differential inequalities based on the theory of subordination and superordination. In this real case study, we found the analytic solutions of q-differential equations. We indicate that the solutions are given in terms of confluent hypergeometric function of the second type and Laguerre polynomial.
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Feehan, Paul M. N., and Manousos Maridakis. "Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (August 1, 2020): 35–67. http://dx.doi.org/10.1515/crelle-2019-0029.

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AbstractWe prove several abstract versions of the Łojasiewicz–Simon gradient inequality for an analytic function on a Banach space that generalize previous abstract versions of this inequality, weakening their hypotheses and, in particular, that of the well-known infinite-dimensional version of the gradient inequality due to Łojasiewicz [S. Łojasiewicz, Ensembles semi-analytiques, (1965), Publ. Inst. Hautes Etudes Sci., Bures-sur-Yvette. LaTeX version by M. Coste, August 29, 2006 based on mimeographed course notes by S. Łojasiewicz, https://perso.univ-rennes1.fr/michel.coste/Lojasiewicz.pdf] and proved by Simon [L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 1983, 3, 525–571]. We prove that the optimal exponent of the Łojasiewicz–Simon gradient inequality is obtained when the function is Morse–Bott, improving on similar results due to Chill [R. Chill, On the Łojasiewicz–Simon gradient inequality, J. Funct. Anal. 201 2003, 2, 572–601], [R. Chill, The Łojasiewicz–Simon gradient inequality in Hilbert spaces, Proceedings of the 5th European-Maghrebian workshop on semigroup theory, evolution equations, and applications 2006, 25–36], Haraux and Jendoubi [A. Haraux and M. A. Jendoubi, On the convergence of global and bounded solutions of some evolution equations, J. Evol. Equ. 7 2007, 3, 449–470], and Simon [L. Simon, Theorems on regularity and singularity of energy minimizing maps, Lect. Math. ETH Zürich, Birkhäuser, Basel 1996]. In [P. M. N. Feehan and M. Maridakis, Łojasiewicz–Simon gradient inequalities for harmonic maps, preprint 2019, https://arxiv.org/abs/1903.01953], we apply our abstract gradient inequalities to prove Łojasiewicz–Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity requirements on maps between closed, Riemannian manifolds. Those inequalities generalize those of Kwon [H. Kwon, Asymptotic convergence of harmonic map heat flow, ProQuest LLC, Ann Arbor 2002; Ph.D. thesis, Stanford University, 2002], Liu and Yang [Q. Liu and Y. Yang, Rigidity of the harmonic map heat flow from the sphere to compact Kähler manifolds, Ark. Mat. 48 2010, 1, 121–130], Simon [L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 1983, 3, 525–571], [L. Simon, Isolated singularities of extrema of geometric variational problems, Harmonic mappings and minimal immersions (Montecatini 1984), Lecture Notes in Math. 1161, Springer, Berlin 1985, 206–277], and Topping [P. M. Topping, Rigidity in the harmonic map heat flow, J. Differential Geom. 45 1997, 3, 593–610]. In [P. M. N. Feehan and M. Maridakis, Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions, preprint 2019, https://arxiv.org/abs/1510.03815v6; to appear in Mem. Amer. Math. Soc.], we prove Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. Those inequalities generalize that of the pure Yang–Mills energy function due to the first author [P. M. N. Feehan, Global existence and convergence of solutions to gradient systems and applications to Yang–Mills gradient flow, preprint 2016, https://arxiv.org/abs/1409.1525v4] for base manifolds of arbitrary dimension and due to Råde [J. Råde, On the Yang–Mills heat equation in two and three dimensions, J. reine angew. Math. 431 1992, 123–163] for dimensions two and three.
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Dissertations / Theses on the topic "Geometric-analytic inequalities"

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Rossi, Andrea. "Borell-Brascamp-Lieb inequalities: rigidity and stability." Doctoral thesis, 2018. http://hdl.handle.net/2158/1125503.

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La tesi è dedicata allo studio delle cosiddette disuguaglianze di Borell-Brascamp-Lieb, note in letteratura come forme funzionali della disuguaglianza di Brunn-Minkowski. L'intento della tesi è duplice: da una parte si prefigge come manuale dettagliato delle disuguaglianze di Borell-Brascamp-Lieb, affrontando varie estensioni e proprietà più o meno note in letteratura; in secondo luogo si concentra sulla questione della stabilità di tali disuguaglianze, citando i risultati più significativi ed esibendo i contributi originali ottenuti, tratti dagli articoli: 1) A. Rossi, P. Salani, Stability for Borell-Brascamp-Lieb inequalities, Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2014-2016 (B. Klartag and E. Milman Eds), Springer Lecture Notes in Mathematics 2169 (2017); 2) A. Rossi, P. Salani, Stability for a strengthened one-dimensional Borell-Brascamp-Lieb inequality, Applicable Analysis (2018). All the Borell-Brascamp-Lieb inequalities can be read as the functional counterparts of the celebrated Brunn-Minkowski inequality, and they have been widely studied in the last decades. The thesis focuses on two main targets. The first is to produce a complete and detailed overview on the results (old and new) on the Borell-Brascamp-Lieb inequalities, the second is to investigate some open questions on the quantitative version of such inequalities. The thesis is divided in 7 chapters. The first five contain the overview on the state of the art, classical and alternative proofs of both Borell-Brascamp-Lieb and Brunn-Minkowski inequalities, theequality cases and some stability results. Chapter 6 and Chapter 7 are devoted to describe the original contributions of the author in the field. Precisely in Chapter 6 a strengthened version of the one dimensional Borell-Brascamp-Liebinequality is proved, while in Chapter 7 the goal is to prove a general quantitative versions of the Borell-Brascamp-Lieb inequalities without concavity assumptions on the involved function. The original results are contained in the following two papers: • A. Rossi, P. Salani, Stability for Borell-Brascamp-Lieb inequalities, Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2014-2016 (B. Klartag - E. Milman Eds), Springer Lecture Notes in Mathematics 2169 (2017); • A. Rossi, P. Salani, Stability for a strengthened one-dimensional Borell-Brascamp- Lieb inequality, Applicable Analysis (2018).
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Books on the topic "Geometric-analytic inequalities"

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Rassias, Themistocles M., and Hari M. Srivastava, eds. Analytic and Geometric Inequalities and Applications. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0.

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1951-, Rassias Themistocles M., and Srivastava H. M, eds. Analytic and geometric inequalities and applications. Dordrecht: Kluwer Academic Publishers, 1999.

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Rassias, Themistocles M. Analytic and Geometric Inequalities and Applications. Dordrecht: Springer Netherlands, 1999.

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Concentration, functional inequalities, and isoperimetry: International workshop, October 29-November 1, 2009, Florida Atlantic University, Boca Raton, Florida. Providence, R.I: American Mathematical Society, 2011.

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Rassias, Themistocles M. Analytic and Geometric Inequalities and Applications. Springer, 2011.

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Rassias, Themistocles M. Analytic and Geometric Inequalities and Applications. Springer, 2012.

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Chavel, Isaac. Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives. Cambridge University Press, 2011.

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Chavel, Isaac. Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics). Cambridge University Press, 2001.

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Sedrakyan, Hayk, and Nairi Sedrakyan. Geometric Inequalities: Methods of Proving. Springer, 2018.

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Sedrakyan, Hayk, and Nairi Sedrakyan. Geometric Inequalities: Methods of Proving. Springer, 2017.

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Book chapters on the topic "Geometric-analytic inequalities"

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Kufner, Alois. "Fractional Order Inequalities of Hardy Type." In Analytic and Geometric Inequalities and Applications, 183–89. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_11.

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Pachpatte, B. G. "On Some Generalized Opial Type Inequalities." In Analytic and Geometric Inequalities and Applications, 301–22. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_18.

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Cheung, Wing-Sum, and Themistocles M. Rassias. "On Multi-Dimensional Integral Inequalities and Applications." In Analytic and Geometric Inequalities and Applications, 53–67. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_5.

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Ando, Tsuyoshi. "Problem of Infimum in the Positive Cone." In Analytic and Geometric Inequalities and Applications, 1–12. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_1.

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Jensen, Shane T., and George P. H. Styan. "Some Comments and a Bibliography on the Laguerre-Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory." In Analytic and Geometric Inequalities and Applications, 151–81. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_10.

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Lakshmikantham, V., and A. S. Vatsala. "Theory of Differential and Integral Inequalities with Initial Time Difference and Applications." In Analytic and Geometric Inequalities and Applications, 191–203. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_12.

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Linden, Hansjörg. "Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials." In Analytic and Geometric Inequalities and Applications, 205–29. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_13.

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Matić, M., C. E. M. Pearce, and J. Pečarić. "Bounds on Entropy Measures for Mixed Populations." In Analytic and Geometric Inequalities and Applications, 231–44. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_14.

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Milovanović, Gradimir V. "Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials." In Analytic and Geometric Inequalities and Applications, 245–64. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_15.

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Noor, Khalida Inayat. "On Alpha-Quasi-Convex Functions Defined by Convolution with Incomplete Beta Functions." In Analytic and Geometric Inequalities and Applications, 265–76. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4577-0_16.

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