*Correspondence: [email protected] 3Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran Full list of author information is available at the end of the article Abstract In this paper, we introduce and consider a new system of generalized nonlinear mixed variational inequalities involving six different nonlinear operators and discuss the existence and uniqueness of s...

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto Lipshitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. In...

This paper is devoted to studying the representation of measures non-generalized compactness, in particular, noncompactness, non-weak compactness and non-super weak etc., defined on Banach spaces its applications. With aid a three-time order-preserving embedding theorem, we show that for every space X, there exist function C(K) some compact Hausdorff K an affine mapping $$\mathbb{T}$$ from supe...

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Let X be a real Hilbert space and J a C functional on X . For x0 ∈ X , r > 0, set S(x0, r) = {x ∈ X : ‖x− x0‖ = r}. Also on the basis of the beautiful theory developed and applied by Schechter and Tintarev in [2], [3], [4] and [5], it is of particular interest to know when the restriction of J to S(0, r) has a unique maximum. The aim of the present paper is to offer a contribution along this di...

Jaggi and Kassay proved that for reflexive Banach spaces X, normal structure is equivalent to the Jaggi fixed point property (i.e. all Jagginonexpansive maps on closed, bounded, convex sets in X have a fixed point); which we note is equivalent to a natural variation: the Jaggi* fixed point property. In the spirit of this result, we prove that for all Banach spaces X, uniform normal structure is...