Monotone generalized $\alpha$-nonexpansive mappings on $C\kern-1ptAT_{p}(0)$ spaces

Emirhan Hacıoǧlu; Faik Gürsoy; Abdul Rahim Khan

doi:10.37863/umzh.v75i7.7188

Emirhan Hacıoǧlu Department of Mathematics, Trakya University, Edirne, Turkey
Faik Gürsoy Department of Mathematics, Adıyaman University, Turkey
Abdul Rahim Khan Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan

DOI: https://doi.org/10.37863/umzh.v75i7.7188

Keywords: $CAT_{p}(0)$ spaces, Monotone Generalized $\alpha -$Non-expansive Mappings, Iterative algorithms, Strong convergence, $\Delta -$convergence

Abstract

UDC 517.5

We examine the existence of fixed points of generalized $\alpha $-nonexpansive mappings on $C\kern-1ptAT_{p}(0)$ spaces. We establish various convergence results for a newly defined algorithm associated with $\alpha $-nonexpansive mappings. We present some illustrative examples to show the efficiency of the proposed algorithm and to support the above-mentioned results. We also define monotone generalized $\alpha $-nonexpansive mappings and prove some existence and convergence results for these mappings.

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