On approximating fixed points of strictly pseudocontractive mappings in metric spaces

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various character...

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Published in:Carpathian Journal of Mathematics 2024-01, Vol.40 (2), p.419-430
Main Authors: SALISU, SANI, BERINDE, VASILE, SRIWONGSA, SONGPON, KUMAM, POOM
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BERINDE, VASILE
SRIWONGSA, SONGPON
KUMAM, POOM
description In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and ex- plore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specif- ically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces.
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title On approximating fixed points of strictly pseudocontractive mappings in metric spaces
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