LAUSR

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 Lpembedded 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.