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In this paper, we first introduce a new class of generalized nonself nonexpansive mappings, called C‐Berinde nonexpansive mappings, and study common best proximity point of two mappings in this class. We propose two hybrid algorithms for finding common best proximity points of two best proximally nonexpansive mappings for which one of them is C‐Berinde nonself nonexpansive mapping. Strong convergence analysis of the proposed methods are discussed in a real Hilbert space. Moreover, we also give a numerical example to support our main results.
In this paper, we introduce new classes of proximal multi-valued contractions
in a metric space and proximal multi-valued nonexpansive mappings in a
Banach space and show the existence of best proximity points for both
classes. Further, for proximal multi-valued nonexpansive mappings, we prove
a best proximity point theorem on starshape sets. As a consequence, we also
obtain some new fixed point theorems. Finally, we give some examples to
illustrate our main results.
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