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...

we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

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.

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the ...

Proximal mappings, which generalize projection mappings, were introduced by Moreau and shown to be valuable in understanding the subgradient properties of convex functions. Proximal mappings subsequently turned out to be important also in numerical methods of optimization and the solution of nonlinear partial differential equations and variational inequalities. Here it is shown that, when a con...

In this paper, three key theorems (the open mapping theorem, the inverse function theorem, and the implicit function theorem) for continuously differentiable maps are shown to hold for nonsmooth continuous maps which are not necessarily Lipschitz continuous. The significance of these extensions is that they are given using generalized Jacobians, called approximate Jacobians. The approximate Jac...

‎the purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex banach space which has a‎ ‎uniformly g^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

In real Hilbert spaceH , from an arbitrary initial point x0 ∈H , an explicit iteration scheme is defined as follows: xn+1 = αnxn + (1 − αn)Tn+1xn,n ≥ 0, where Tn+1xn = Txn − λn+1μF(Txn), T :H →H is a nonexpansive mapping such that F(T) = {x ∈ K : Tx = x} is nonempty, F :H →H is a η-strongly monotone and k-Lipschitzian mapping, {αn} ⊂ (0,1), and {λn} ⊂ [0,1). Under some suitable conditions, the ...