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Journal articles on the topic 'Multivalued maps'

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Published: 14 March 2023

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1

Ślosarski, Mirosław. "Metrizable space of multivalued maps." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 20, no. 1 (January 1, 2021): 77–93. http://dx.doi.org/10.2478/aupcsm-2021-0006.

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Abstract In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homotopy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric.

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2

Gonzalez, Jorge A., and Lindomar B. De Carvalho. "Analytical Solutions to Multivalued Maps." Modern Physics Letters B 11, no. 12 (May 20, 1997): 521–30. http://dx.doi.org/10.1142/s0217984997000633.

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We present explicit solutions for a class of chaotic maps. The return-maps generated by a special class of chaotic functions can be multivalued, or even they can represent an erratic set of points. In some cases the produced time series can have an increasing time-dependent maximum Lyapunov exponent. We discuss some applications of the obtained results. In particular, we present a chaotic lattice model for the investigation of the propagation of carriers in the presence of disorder.

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3

SIMONS, S. "Cyclical coincidences of multivalued maps." Journal of the Mathematical Society of Japan 38, no. 3 (July 1986): 515–25. http://dx.doi.org/10.2969/jmsj/03830515.

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4

Joanna Czarnowska. "Perfect Roads for Multivalued Maps." Real Analysis Exchange 31, no. 2 (2006): 365. http://dx.doi.org/10.14321/realanalexch.31.2.0365.

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5

Latif, Abdul, Taqdir Husain, and Ismat Beg. "Fixed point of nonexpansive type andK-multivalued maps." International Journal of Mathematics and Mathematical Sciences 17, no. 3 (1994): 429–35. http://dx.doi.org/10.1155/s016117129400061x.

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6

Andres, Jan. "Chaos for multivalued maps and induced hyperspace maps." Chaos, Solitons & Fractals 138 (September 2020): 109898. http://dx.doi.org/10.1016/j.chaos.2020.109898.

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7

Giraldo, Antonio. "Shape Fibrations, Multivalued Maps and Shape Groups." Canadian Journal of Mathematics 50, no. 2 (April 1, 1998): 342–55. http://dx.doi.org/10.4153/cjm-1998-018-7.

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AbstractThe notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of thesemaps–which agreewith shape fibrations having totally disconnected fibers–with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated.

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8

Crabb, M. C. "Nielsen-Reidemeister indices for multivalued maps." Bulletin of the Belgian Mathematical Society - Simon Stevin 24, no. 4 (December 2017): 483–99. http://dx.doi.org/10.36045/bbms/1515035003.

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9

Raitums, U. "On the Projections of Multivalued Maps." Journal of Optimization Theory and Applications 92, no. 3 (March 1997): 633–60. http://dx.doi.org/10.1023/a:1022611608062.

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10

Sánchez-Gabites, J. J., and J. M. R. Sanjurjo. "Multivalued maps, selections and dynamical systems." Topology and its Applications 155, no. 8 (April 2008): 874–82. http://dx.doi.org/10.1016/j.topol.2006.10.016.

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11

Górniewicz, L., S. A. Marano, and M. Slosarski. "Fixed points of contractive multivalued maps." Proceedings of the American Mathematical Society 124, no. 9 (1996): 2675–83. http://dx.doi.org/10.1090/s0002-9939-96-03265-0.

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12

Latif, A., and W. A. Albar. "Fixed point results for multivalued maps." International Journal of Contemporary Mathematical Sciences 2 (2007): 1129–36. http://dx.doi.org/10.12988/ijcms.2007.07114.

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13

Husain, T., and Abdul Latif. "Fixed points of multivalued nonexpansive maps." International Journal of Mathematics and Mathematical Sciences 14, no. 3 (1991): 421–30. http://dx.doi.org/10.1155/s0161171291000558.

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Fixed point theorems for multivalued contractive-type and nonexpansive-type maps on complete metric spaces and on certain closed bounded convex subsets of Banach spaces have been proved. They extend some known results due to Browder, Husain and Tarafdar, Karlovitz and Kirk.

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14

Latif, Abdul, and Ian Tweddle. "Some results on coincidence points." Bulletin of the Australian Mathematical Society 59, no. 1 (February 1999): 111–17. http://dx.doi.org/10.1017/s0004972700032652.

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In this paper we prove some coincidence point theorems for nonself single-valued and multivalued maps satisfying a nonexpansive condition. These extend fixed point theorems for multivalued maps of a number of authors.

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15

Ewert, Janina. "Quasicontinuity and related properties of functions and multivalued maps." Mathematica Bohemica 120, no. 4 (1995): 393–403. http://dx.doi.org/10.21136/mb.1995.126086.

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16

Sanjurjo, José M. R. "Selections of multivalued maps and shape domination." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 3 (May 1990): 493–99. http://dx.doi.org/10.1017/s0305004100068778.

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AbstractSome results are presented which establish connections between shape theory and the theory of multivalued maps. It is shown how to associate an upper-semi-continuous multivalued map F: X → Y to every approximative map f = {fk, X → Y} in the sense of K. Borsuk and it is proved that, in certain circumstances, if F is ‘small’ and admits a selection, then the shape morphism S(f) is generated by a map, and if F admits a coselection then S(f) is a shape domination.

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17

Andres, Jan. "Chaos for Differential Equations with Multivalued Impulses." International Journal of Bifurcation and Chaos 31, no. 07 (June 15, 2021): 2150113. http://dx.doi.org/10.1142/s0218127421501133.

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The deterministic chaos in the sense of a positive topological entropy is investigated for differential equations with multivalued impulses. Two definitions of topological entropy are examined for three classes of multivalued maps: [Formula: see text]-valued maps, [Formula: see text]-maps and admissible maps in the sense of Górniewicz. The principal tool for its lower estimates and, in particular, its positivity are the Ivanov-type inequalities in terms of the asymptotic Nielsen numbers. The obtained results are then applied to impulsive differential equations via the associated Poincaré translation operators along their trajectories. The main theorems for chaotic differential equations with multivalued impulses are formulated separately on compact subsets of Euclidean spaces and on tori. Several illustrative examples are supplied.

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18

Singh, S. L., and S. N. Mishra. "Coincidences and fixed points of reciprocally continuous and compatible hybrid maps." International Journal of Mathematics and Mathematical Sciences 30, no. 10 (2002): 627–35. http://dx.doi.org/10.1155/s0161171202007536.

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It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

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19

Shehu, Yekini. "Convergence Theorems for Finite Family of Multivalued Maps in Uniformly Convex Banach Spaces." ISRN Mathematical Analysis 2011 (August 28, 2011): 1–13. http://dx.doi.org/10.5402/2011/576108.

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We introduce a new iterative process to approximate a common fixed point of a finite family of multivalued maps in a uniformly convex real Banach space and establish strong convergence theorems for the proposed process. Furthermore, strong convergence theorems for finite family of quasi-nonexpansive multivalued maps are obtained. Our results extend important recent results.

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20

Agarwal, Ravi P., and Donal O'regan. "A Fixed Point Theorem of Leggett–Williams Type with Applications to Single- and Multivalued Equations." gmj 8, no. 1 (March 2001): 13–25. http://dx.doi.org/10.1515/gmj.2001.13.

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21

Danilov, L. I. "On almost periodic sections of multivalued maps." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, no. 2 (April 2008): 34–41. http://dx.doi.org/10.20537/vm080213.

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22

Bin Dehaish, B. A., and Abdul Latif. "Fixed point results for multivalued contractive maps." Fixed Point Theory and Applications 2012, no. 1 (2012): 61. http://dx.doi.org/10.1186/1687-1812-2012-61.

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23

Hussain, N., and A. R. Khan. "Random fixed points of multivalued -nonexpansive maps." Random Operators and Stochastic Equations 11, no. 3 (September 1, 2003): 243–54. http://dx.doi.org/10.1163/156939703771378590.

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24

Izydorek, Marek, and Jan Jaworowski. "Parametrized Borsuk-Ulam theorems for multivalued maps." Proceedings of the American Mathematical Society 116, no. 1 (January 1, 1992): 273. http://dx.doi.org/10.1090/s0002-9939-1992-1112493-0.

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25

ORegan, Donal. "Random fixed point theory for multivalued maps." Stochastic Analysis and Applications 17, no. 4 (January 1999): 597–607. http://dx.doi.org/10.1080/07362999908809623.

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26

Donchev, Tzanko. "Properties of one-sided Lipschitz multivalued maps." Nonlinear Analysis: Theory, Methods & Applications 49, no. 1 (April 2002): 13–20. http://dx.doi.org/10.1016/s0362-546x(00)00244-3.

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27

Lipski, Tadeusz. "MULTIVALUED MAPS OF COUNTABLY PARACOMPACT BITOPOLOGICAL SPACES." Demonstratio Mathematica 18, no. 4 (October 1, 1985): 1143–52. http://dx.doi.org/10.1515/dema-1985-0415.

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28

Chuan, Hu Shou, Klaus Deimling, and Jan Prüβ. "Fixed points of weakly inward multivalued maps." Nonlinear Analysis: Theory, Methods & Applications 10, no. 5 (May 1986): 465–69. http://dx.doi.org/10.1016/0362-546x(86)90051-9.

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29

Lucio, P. S., G. Lambar�, and A. Hanyga. "3D multivalued travel time and amplitude maps." Pure and Applied Geophysics PAGEOPH 148, no. 3-4 (1996): 449–79. http://dx.doi.org/10.1007/bf00874575.

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30

Mehmood, Nayyar, Akbar Azam, and Ismat Beg. "Fixed points of Edelstein-type multivalued maps." Rendiconti del Circolo Matematico di Palermo (1952 -) 63, no. 3 (September 9, 2014): 399–407. http://dx.doi.org/10.1007/s12215-014-0166-6.

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31

Benedetti, Irene, and Pietro Zecca. "Applications on variational inequalities involving multivalued maps." PAMM 7, no. 1 (December 2007): 1060101–2. http://dx.doi.org/10.1002/pamm.200700491.

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32

Fenille, Marcio Colombo. "A reverse viewpoint on the upper semicontinuity of multivalued maps." Mathematica Bohemica 138, no. 4 (2013): 415–23. http://dx.doi.org/10.21136/mb.2013.143514.

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33

Vijayaraju, P., and R. Hemavathy. "Generalized $ f $-nonexpansive R-subweakly commuting multivalued maps." Tamkang Journal of Mathematics 38, no. 4 (December 31, 2007): 307–12. http://dx.doi.org/10.5556/j.tkjm.38.2007.64.

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34

Agarwal, Ravi P., Donal O'Regan, and Mohamed-Aziz Taoudi. "FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES." Asian-European Journal of Mathematics 04, no. 03 (September 2011): 373–87. http://dx.doi.org/10.1142/s1793557111000307.

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We present new fixed point theorems for multivalued [Formula: see text]-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

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35

Mınak, Gülhan, Özlem Acar, and Ishak Altun. "Multivalued Pseudo-Picard Operators and Fixed Point Results." Journal of Function Spaces and Applications 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/827458.

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We introduce the concept of multivalued pseudo-Picard (MPP) operator on a metric space. This concept is weaker than multivalued weakly Picard (MWP) operator, which is given by M. Berinde and V. Berinde (2007). Then, we give both fixed point results and examples for MPP operators. Also, we obtain some ordered fixed point results for multivalued maps as application.

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36

Kas’yanov, P. O., V. S. Mel’nik, and L. Toscano. "Multivalued penalty method for evolution variational inequalities with λ 0-pseudomonotone multivalued maps." Nonlinear Oscillations 10, no. 4 (October 2007): 0. http://dx.doi.org/10.1007/s11072-008-0006-8.

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37

O’Regan, Donal. "Coincidence Continuation Theory for Multivalued Maps with Selections in a Given Class." Axioms 9, no. 2 (April 10, 2020): 37. http://dx.doi.org/10.3390/axioms9020037.

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38

Alsaedi, Ahmed, Bashir Ahmad, Madeaha Alghanmi, and Sotiris K. Ntouyas. "On a Generalized Langevin Type Nonlocal Fractional Integral Multivalued Problem." Mathematics 7, no. 11 (October 25, 2019): 1015. http://dx.doi.org/10.3390/math7111015.

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We establish sufficient criteria for the existence of solutions for a nonlinear generalized Langevin-type nonlocal fractional-order integral multivalued problem. The convex and non-convex cases for the multivalued map involved in the given problem are considered. Our results rely on Leray–Schauder nonlinear alternative for multivalued maps and Covitz and Nadler’s fixed point theorem. Illustrative examples for the main results are included.

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39

Ślosarski, Mirosław. "Multi-invertible maps and their applications." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 18, no. 1 (December 1, 2019): 35–52. http://dx.doi.org/10.2478/aupcsm-2019-0003.

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Abstract In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of r-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.

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40

Gallegos, Claudio A., and Hernán R. Henríquez. "Fixed points of multivalued maps under local Lipschitz conditions and applications." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 3 (January 29, 2019): 1467–94. http://dx.doi.org/10.1017/prm.2018.151.

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AbstractIn this work we are concerned with the existence of fixed points for multivalued maps defined on Banach spaces. Using the Banach spaces scale concept, we establish the existence of a fixed point of a multivalued map in a vector subspace where the map is only locally Lipschitz continuous. We apply our results to the existence of mild solutions and asymptotically almost periodic solutions of an abstract Cauchy problem governed by a first-order differential inclusion. Our results are obtained by using fixed point theory for the measure of noncompactness.

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41

O'Regan, Donal, and Naseer Shahzad. "Approximation and fixed point theorems for countable condensing composite maps." Bulletin of the Australian Mathematical Society 68, no. 1 (August 2003): 161–68. http://dx.doi.org/10.1017/s0004972700037515.

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42

O’Regan, Donal. "Maximal Type Elements for Families." Symmetry 13, no. 12 (November 29, 2021): 2269. http://dx.doi.org/10.3390/sym13122269.

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In this paper, we present a variety of existence theorems for maximal type elements in a general setting. We consider multivalued maps with continuous selections and multivalued maps which are admissible with respect to Gorniewicz and our existence theory is based on the author’s old and new coincidence theory. Particularly, for the second section we present presents a collectively coincidence coercive type result for different classes of maps. In the third section we consider considers majorized maps and presents a variety of new maximal element type results. Coincidence theory is motivated from real-world physical models where symmetry and asymmetry play a major role.

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43

O’Regan, Donal. "Topological Transversality Coincidence Theory for Multivalued Maps with Selections in a Given Class." Analele Universitatii "Ovidius" Constanta - Seria Matematica 29, no. 1 (March 1, 2021): 201–9. http://dx.doi.org/10.2478/auom-2021-0013.

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44

Singh, S. L., Raj Kamal, Renu Chugh, and Swami Nath Mishra. "New common fixed point theorems for multivalued maps." Applied General Topology 15, no. 2 (May 23, 2014): 111. http://dx.doi.org/10.4995/agt.2014.2815.

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45

Danilov, L. I. "On Besicovitch almost periodic selections of multivalued maps." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, no. 1 (January 2008): 97–120. http://dx.doi.org/10.20537/vm080106.

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46

Al-Mezel, Saleh Abdullah. "Fixed point results for multivalued contractive type maps." Journal of Nonlinear Sciences and Applications 09, no. 03 (March 31, 2016): 1373–81. http://dx.doi.org/10.22436/jnsa.009.03.61.

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47

Alkhammash, Aljazi M., Afrah A. N. Abdou, and Abdul Latif. "Fixed point results for generalized contractive multivalued maps." Journal of Nonlinear Sciences and Applications 10, no. 05 (May 4, 2017): 2359–65. http://dx.doi.org/10.22436/jnsa.010.05.08.

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48

Czarnowska. "On the Intermediate Value Property of Multivalued Maps." Real Analysis Exchange 17, no. 1 (1991): 77. http://dx.doi.org/10.2307/44152193.

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49

Dzedzej, Zdzisław, and Tomasz Gzella. "Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree." Mathematics 8, no. 8 (August 1, 2020): 1262. http://dx.doi.org/10.3390/math8081262.

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Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarkés generalized gradient of f. This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient mappings.

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50

Kassay, G., and J. Kolumban. "Multivalued Parametric Variational Inequalities with α-Pseudomonotone Maps." Journal of Optimization Theory and Applications 107, no. 1 (October 2000): 35–50. http://dx.doi.org/10.1023/a:1004600631797.

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