Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong c...

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of theMann iterationmethod and the Ishikawa iterationmethod for φ-pseudocontractive operators in nonempty closed convex subsets of unifor...

We show differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally antiLipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably...

It is known that a uniformly convex Banach space is reflexive and strictly convex. E is said to be smooth provided limt→ ‖x+ty‖–‖x‖ t exists for all x, y ∈UE . It is also said to be uniformly smooth if the limit is attained uniformly for all x, y ∈UE . It is well known that if E* is strictly convex, then J is single valued; if E* is reflexive, and smooth, then J is single valued and demicontin...

A new system of nonlinear fuzzy variational inclusions involving A, η -accretive mappings in uniformly smooth Banach spaces is introduced and studiedmany fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η -accretive operator due to Lan et al. and Nadler’s fixed points theorem for set-val...

* Correspondence: poom. [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s University, of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand Full list of author information is available at the end of the article Abstract In this article, we introduce a new iterative scheme for finding a common element of the set of fixed points of strongly relatively nonexp...