Implicit Function Theorems for Nondifferentiable Mappings

Implicit Function Theorems for Nondifferentiable Mappings1

Sufficient conditions are given for a mapping to be γ -G inverse differentiable. Constrained implicit function theorems for γ -G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed subset. A theorem without assuming the γ -G inverse differentiability in a finite-dimensional space is also presented.

Convergence theorems of an implicit iteration process for asymptotically pseudocontractive mappings

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.

Convergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.

Point Theorems for Compatible Mappings Satisfying an Implicit Relation

Implicit Function Theorems for M-accretive and Locally Accretive Set-valued Mappings

In this paper we elaborate new methods to the theory of parametric generalized equations governed by accretive mappings. Two implicit function theorems will be proved, one for m-accretive and another for locally accretive and continuous set-valued mappings. Making use of the theorem for m-accretive mappings we will study parametric nonlinear evolution problems. It will be also shown that there ...