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Fixed Points Theorems for Multivalued Mappings

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

In this article we discuss the solvability of some class of multivalued inclusions in Euclidean spaces based on a generalization of the “conditions of an acute angle”. As corollary we receive fixed-point theorems for multivalued mappings (continuous and non continuous).

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References

  1. M.A. Krasnoselskii, Topological Method in Theory of Nonlinear Integral Equations, (1956). Moscow, Gostekhizdat (Russian), 392 pp.

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  6. Y. Zelinskii, M. Tkachuk, B. Klishchuk, Fixed point theorems for multivalued mappings. Zb. Prats Inst. Mat. NAN Ukr. (Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine) 9(2), 175–179 (2012) (Russian)

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Acknowledgement

These results is partially supported by the research work grant NAS Ukraine—Tubitek (Turkey), No. 110T558. The author is grateful to Professor Kamal Soltanov for his valuable suggestion in studying a fixed point behavior in a non continuous case and to my students Bogdan Klishchuk and Maxim Tkachuk for active discussions of all proposed results.

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Authors and Affiliations

  1. Institute of mathematics NAS of Ukraine, Tereshchenkivska str. 3, Kyiv, 01601, Ukraine

    Yuri Zelinskii

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  1. Yuri Zelinskii
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Correspondence to Yuri Zelinskii .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Zelinskii, Y. (2015). Fixed Points Theorems for Multivalued Mappings. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_39

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