TY - JOUR

T1 - Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces

AU - Zegeye, Habtu

AU - Wega, Getahun Bekele

PY - 2020/8/11

Y1 - 2020/8/11

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85089291339

JO - Rendiconti del Circolo Matematico di Palermo

JF - Rendiconti del Circolo Matematico di Palermo

SN - 0009-725X

ER -