Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces

Habtu Zegeye, Getahun Bekele Wega

Research output: Contribution to journalArticle

Abstract

Let E be a real reflexive Banach space with its dual E and f be a proper, convex and lower-semi-continuous function on E. The purpose of this paper is to introduce and study a new class of mappings from E into E called f-pseudocontractive mappings with the notion of f-fixed points. In the case that E is a real reflexive Banach space and f is a strongly coercive, bounded and uniformly Fréchet differentiable Legendre function which is strongly convex on bounded subsets of E, a sequence is constructed which converges strongly to a common f-fixed point of two f-pseudocontractive mappings. As a consequence, we obtain a scheme which converges strongly to a common zero of monotone mappings. Furthermore, this analog is applied to approximate solutions to convex optimization problems. Our results improve and generalize many of the results in the literature.

Original languageEnglish
Number of pages24
JournalRendiconti del Circolo Matematico di Palermo
Publication statusAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces'. Together they form a unique fingerprint.

  • Cite this