Existence of fixed points of weak enriched nonexpansive mappings in Banach spaces

Abstract

In this work, we introduce and study a new class of weak enriched nonexpasive mappings which is a generalization of enriched nonexpansive mappings provided by Berinde [Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces], Carpathian J. Math., 35 (2019), No. 3, 293–304]. This class of mappings generalizes several important classes of nonlinear mappings. We prove some fixed point theorems regarding this kind of mappings which extend some important results in [Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293–304]. Moreover, some examples, to ensure the existence of these mappings and support our main theorems, are also given.

Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences

“…4. The technique of proof used in the present paper, essentially based on the concepts of graphic contraction and approximate fixed point sequence, could also be nontrivially applied to other classes of self and nonself single-valued mappings in the literature on metric fixed point theory, see [5,[7][8][9][10][11][12]14,20,23,28,31,36,38,39,42,44,46,50,60,61,63] etc. 5.…”