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Generalized strongly vector equilibrium problem for set-valued mappings

Ahmad Rais (Aligarh Muslim University, Department of Mathematics, Aligarh, India)
Rahaman Mijanur (Aligarh Muslim University, Department of Mathematics, Aligarh, India)

In this paper, we introduce and study a generalized strongly vector equilibrium problem for set-valued mappings in real Banach spaces. Using Minty type lemma and KKM-Fan theorem as basic tools, we prove existence theorems for generalized strongly vector equilibrium problem with and without monotonicity, respectively. Some examples are given.

Keywords: Vector equilibrium problem, Strong pseudomonotone mapping, C-quasiconvex-like mapping, KKM mapping