Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mapping A of K , we denote by Lip(A) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self-mappings of K . We consider the set of all sequences {At}t=1 of such selfmappings with the property limsupt→∞ Lip(At) ≤ 1. Endowing it with an appropriate...

* Correspondence: [email protected]. edu.cn School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, People’s Republic of China Full list of author information is available at the end of the article Abstract In this article, we introduce the concept of nonself uniformly quasi-Lipschitzian mapping and consider a new iterative scheme with errors to converge t...

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. ...

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

We show some stability and convergence theorems of the modified Ishikawa iterative sequence with errors for a strongly successively pseudocontractive and strictly asymptotically pseudocontractive mapping in a real Banach space. Additionally, we prove that if T is a uniformly Lipschitzian strongly accretive mapping, the modified Ishikawa iteration sequence with errors converges strongly to the u...

In this paper, the results of a quadruple coincidence point (QCP) are established for commuting mapping in setting fuzzy metric spaces (FMSs) without using partially ordered set. addition, several related presented order to generalize some prior findings area. Finally, support and enhance our theoretical ideas, non-trivial examples applications finding unique solution Lipschitzian integral syst...

Abstract: Many hypersurfaces ω in R can be viewed as a subset of the boundary Γ of an open subset Ω of R . In such cases, the gradient and Hessian matrix of the associated oriented distance function bΩ to the underlying set Ω completely describe the normal and the N fundamental forms of ω, and a fairly complete intrinsic theory of Sobolev spaces on C-hypersurfaces is available in Delfour (2000)...

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

In this article, we prove strong convergence of sequence generated by the following iteration sequence for a class of Lipschitzian pseudocontractive mapping T: x n+1 = β n u + (1 − β n)[α n Tx n + (1 − α n)x n ] whenever {a n } and {b n } satisfy the appropriate conditions.