TY - JOUR
T1 - Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces
AU - Zegeye, Habtu
AU - Wega, Getahun Bekele
N1 - Publisher Copyright:
© 2020, Springer-Verlag Italia S.r.l., part of Springer Nature.
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.
UR - http://www.scopus.com/inward/record.url?scp=85089291339&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85089291339&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85089291339
SN - 0009-725X
VL - 70
SP - 1139
EP - 1162
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 3
ER -