In this paper we prove several existence results for a general class of systems of nonlinear hemivariational inequalities by using a fixed point theorem of Lin [21]. Our analysis includes both the cases of bounded and unbounded closed convex subsets in real reflexive Banach spaces. In the last section we apply the abstract results obtained to extend some results concerning nonlinear hemivariati...

* Correspondence: [email protected]. th Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Abstract In this paper, we introduce the modified general iterative approximation methods for finding a common fixed point of nonexpansive semigroups which is a unique solution of some variational inequalities. The strong convergence theorems are established in the...

In this paper, some existence theorems for the mixed quasi-variational-like inequalities problem in a reflexive Banach space are established. The auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution for the mixed quasi-variational-like inequalities problem. Consequently, not only the existence of theorems of the mixed...

In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke’s generalized directional derivative in reflexive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke’s generalized directional derivative under different monotonicity assumptions, we establish two kinds of co...

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved. A class o...

In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality p...

Let M and I, be (nonlinear) operators in a reflexive Banach space B for which Rg(M + L) = B and j(Mx My) i~(Lx Ly)( > / Mx My / for all 01 > 0 and pairs s, y in D(M) n D(L). Then there is a unique solution of the Cauchy problem (Mu(t))’ + Lu(t) = 0, Mu(O) = v0 . When M and L are realizations of elliptic partial differential operators in space variables, this gives existence and uniqueness of ge...