8 research outputs found

    Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces

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    By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solutions of the generalized set-valued variational-like inclusions and the convergence criteria of the two iterative algorithms for the generalized set-valued variational-like inclusions in reflexive Banach spaces. The results presented in this paper are new and are an extension of the corresponding results in this direction

    Existence of Solutions and Algorithm for a System of Variational Inequalities

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    We obtain some existence results for a system of variational inequalities (for short, denoted by SVI) by Brouwer fixed point theorem. We also establish the existence and uniqueness theorem using the projection technique for the SVI and suggest an iterative algorithm and analysis convergence of the algorithm

    Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces

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    We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding's technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate solutions of the generalized nonlinear mixed variational-like inequality, and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend, and unify many known results in this area
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