In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...

and Applied Analysis 3 where R is the set of all real numbers; in particular, J(−x) = −J(x) for all x ∈ E ([28]). We say that a Banach space E has a weakly sequentially continuous duality mapping if there exists a gauge function φ such that the duality mapping Jφ is single valued and continuous from the weak topology to the weak topology; that is, for any {xn} ∈ E with xn ⇀ x, Jφ(xn) ∗ ⇀ Jφ(x)....

Let E be a real q-uniformly smooth Banach space whose duality map is weakly sequentially continuous. Let T : E → E be a nonexpansive mapping with F (T ) 6= ∅. Let A : E → E be an η-strongly accretive map which is also κ-Lipschitzian. Let f : E → E be a contraction map with coefficient 0 < α < 1. Let a sequence {yn} be defined iteratively by y0 ∈ E, yn+1 = αnγf(yn) + (I − αnμA)Tyn, n ≥ 0, where ...

Let X be a real Banach space with a normalized duality mapping uniformly norm-to-weak continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping JΦ with gauge φ. Let f be an α-contraction and {Tn} a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes xn+1 = αnf(xn) + (1− αn)Tnxn (1) with a general theorem a...

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.

The aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in $L$-fuzzy topological spaces