In this paper,we study the Ishikawa iterative sequences with errors for Lipschitzian strongly pseudo-contractive operator in arbitrary real Banach spaces. Our results improve the results obtained previously by C. E. Chidume [3] and Zeng [9].

The approximate subdifferential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdifferentiability might be related to its nonconvexity. This is motivation to study some topological properties more in detail. As the main result, it is shown that any weakly compact subset of any Hilbert space may be ...

Recommended by Mohamed Khamsi Let S be a left amenable semigroup, let S {T s : s ∈ S} be a representation of S as Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition, let {μn} be a strongly left regular sequence of means defined on an S-stable subspace of l∞ S , let f be a contraction on C, and let {αn}, {βn}, and...

In this note we study the differentiability with respect to time-parameter of semigroups consisting Lipschitzian or smooth self-mappings a domain in Banach space.

The Ishikawa iterative sequences with errors are studied for Lipschitzian strongly pseudo-contractive operators in arbitrary real Banach spaces; some well-known results of Chidume (1998) and Zeng (2001) are generalized.

A companion for the Ostrowski and the generalised trapezoid inequalites for various classes of functions, including functions of bounded variation, Lipschitzian, convex and absolutely continuous functions is established. Applications for weighted means are also given.

The approximate subdiierential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdiierentiability might be related to its non-convexity. This motivates to study some topological properties more in detail. As the main result, it is shown that in a Hilbert space setting each weakly compact set may be o...

The concept of compactly epi-Lipschitzian (CEL) sets in locally convex topological spaces was introduced by Borwein and Strojwas [6]. It is an extension of Rockafellar’s concept of epi-Lipschitzian sets [36]. An advantage of the CEL property is that it always holds in finite dimensional spaces and, in contrast to its epi-Lipschitzian predecessor, makes it possible to recapture much of the detai...

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in o...

* Correspondence: [email protected] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract The purpose of this paper is to introduce a new system of general nonlinear regularized nonconvex variational inequalities and verify the equivalence between the proposed system and f...