Strong convergence of an inertial Halpern type algorithm in Banach spaces

被引：0

作者：

Ranjbar, Sajad ^{[1
]}

机构：

[1] Higher Educ Ctr Eghlid, Dept Math, Eghlid, Iran

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2023年 / 72卷 / 03期

关键词：

Fixed point; Strong convergence; Iterative methods; Halpern iteration; Accretive operator; MAXIMAL MONOTONE-OPERATORS; COMMON FIXED-POINTS; ACCRETIVE-OPERATORS; NONEXPANSIVE RETRACTS; ASYMPTOTIC-BEHAVIOR; THEOREMS; SEMIGROUPS; MAPPINGS; ZEROS;

D O I：

10.1007/s12215-022-00748-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we obtain the strong convergence of the new modified Halpern iteration process x(n+1) = alpha(n)u+(1-alpha(n))TnP(x(n) + theta(n)(x(n) - x(n-1))), n = 1,2,3, ... , to a common fixed point of {T-n}, where {T-n}(n=1)(infinity) is a family of nonexpansive mappings on the closed and convex subset C of a Banach space X, P : X -> C is a nonexpansive retraction, {alpha(n)} subset of [0, 1] and {theta(n)} subset of R+. Some applications of this result are also presented.

引用

页码：1561 / 1570

页数：10

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