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In this paper, we introduce and study a generalized variational-like inequality problem in topological vector spaces. We prove an existence result for generalized variational-like inequality problem using KKM-theorem and we show its equivalence with another variational-like inequality problem using relaxed η-α-monotone mapping. Our result improve and extend some corresponding results of [1, 9, 10, 17, 22, 23]. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to study a new class of fuzzy nonlinear set-valued variational inclusions in real Banach spaces. By using the fuzzy resolvent operator techniques for -accretive mappings, we establish the equivalence between fuzzy nonlinear set-valued variational inclusions and fuzzy resolvent operator equation problem. Applying this equivalence and Nadler’s theorem, we suggest some iterative algorithms for solving fuzzy nonlinear set-valued variational inclusions in real Banach spaces. By using the inequality of Petryshyn, the existence of solutions for these kinds of fuzzy nonlinear set-valued variational inclusions without compactness is proved and convergence criteria of iterative sequences generated by the algorithm are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Solvabilities of generalized vector variational-type inequalities (GVVTI) are discussed in this work. First, the solvability of GVVTI without monotone assumption for mappings is considered in (reflexive) Banach spaces by using Brouwer fixed point theorem (Browder fixed point theorem). Second, the solvability of GVVTI with monotone assumption for mappings is considered in reflexive Banach spaces by using Ky Fan lemma. [Copyright &y& Elsevier]

Abstract: In this work, we present some new existence theorems for solutions for a new class of generalized vector -implicit complementarity problems and the corresponding generalized vector -implicit variational inequality problems by using the Fan–KKM Theorem under some suitable assumptions without monotonicity, and establish the equivalence between those problems in Banach spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a vector version of Minty''s lemma and obtain existence theorems for two kinds of variational-like inequality. A fixed point theorem is also discussed. [Copyright &y& Elsevier]

The study was conducted with the aim to find out random variational-like inclusion involving relaxed monotone, random operators in Hilbert space and construct a new iterative algorithm. The study also proves the existence of random solution of random variational-like inclusion problem and convergence of random iterative sequences generated by random iterative algorithm. The results in this paper unify, improve and extend some well-known results from the literature. [ABSTRACT FROM AUTHOR]