On the existence of solutions of extended generalized variational inequalities in Banach spaces

다국어 초록 (Multilingual Abstract)

In this paper, we study the following extended generalized variational inequality problem, introduced by Noor (for short, EGVI) : Given a closed convex subset K in q-uniformly smooth Banach space B, three nonlinear mappings T :K → B*, g:K → K, h:K → K and a vector
ξ ∈ B*, find x ∈ K, h(x) ∈ K such that [수식], for all y ∈ K, g(y)∈K.[see [2]: M. Aslam Noor, Extended general variational inequalities, Appl. Math. Lett. 22 (2009) 182-186.] By using sunny nonexpansive retraction QK and the well-known Banach's fixed point principle, we prove existence results for solutions of (EGVI). Our results extend some recent results from the literature.

참고문헌 (Reference)

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