FIXED POINT THEOREMS FOR GENERALIZED (α, β)-S-NONEXPANSIVE MAPPINGS WITHOUT DEMI-CLOSEDNESS PRINCIPLE IN BANACH SPACES

Résumé fourni par la source

We introduce a new class of nonlinear mappings called generalized $(\alpha,\beta)$-$S$-nonexpansive mappings and show that this class of nonlinear mappings can be considered as an extension of of nonexpansive, firmly-nonexpansive and $(\alpha,\beta)$-nonexpansive mappings. Beyond the continuity assumption on the mappings and without using the classical demiclosedness principle, we will verify new existence and convergence results for these mappings in Banach spaces. To illustrate the results, we include some examples in the paper.

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