Fixed points of generalized hybrid mappings on L2-embedded sets in Banach spaces


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	Fixed points of generalized hybrid mappings on L₂-embedded sets in Banach spaces


	Fixed Point Theory, Volume 20, No. 1, 2019, 203-210, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.13 Authors: A. Jabbari and R. Keshavarzi Abstract: In this paper, first we generalize the notion of L-embedded sets in Banach spaces, defined by A.T.-M. Lau and Y. Zhang in “Fixed point properties for semigroups of nonlinear mappings and amenability”, Journal of Functional Analysis, 263 (2012), pp. 2949-2977, to the notion of L_p-embedded sets (p > 0). Then, for a given generalized hybrid mapping T, we introduce the concepts of T-Chebyshev radius and T-Chebyshev center, generalizing the concepts of Chebyshev radius and Chebyshev center for nonexpansive mappings. Finally, we study the existence of fixed points of generalized hybrid mappings on L₂-embedded subsets of a Banach space by using the notions of T-Chebyshev radius and T-Chebyshev center. Key Words and Phrases: fixed point, generalized hybrid mapping, L₂ − embedded set, Chebyshev center. 2010 Mathematics Subject Classification: 47H10, 37C25. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents