On generalized nonlinear variational-like inequality problems

Existence of Solutions to Generalized Vector Quasi-equilibrium Problems with Set-Valued Mappings

“…Remark3.1 Theorem 3.1 and Theorem 3.2 improve and extend the corresponding results of [4][5][6][7]. ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (11371070).…”

“…Based on these works, Gao and Feng [7] considered a class of generalized vector quasi-variational-like inequality problems and utilize the maximal element theorem with an sequence to prove the existence of its solutions in the setting of locally convex topological vector space(in short, locally convex spaces). Inspired and motivated by the above research, in this paper, we introduce a new class of generalized vector quasiequilirium problems and follow the idea of [7], we obtain the existence results of its solutions in the setting of locally convex space, which are very interesting and improve and extend the corresponding results of [4][5][6][7].…”

“…Recently, Peng and Rong [4], Ahmad and Irfan [5] and Xiao et al [6] proved some existence theorems of solutions to a class of generalized nonlinear variational inequalities. Based on these works, Gao and Feng [7] considered a class of generalized vector quasi-variational-like inequality problems and utilize the maximal element theorem with an sequence to prove the existence of its solutions in the setting of locally convex topological vector space(in short, locally convex spaces).…”

Existence results for generalized nonlinear vector variational-like inequalities with set-valued mapping

“…In 1966, Browder [5] first formulated and proved the basic existence theorems of solutions to a class of nonlinear variational inequalities. Very recently, Liu et al [6], Zhao et al [7] and Ahmad et al [8] extended Browder's results to more generalized nonlinear variational inequalities.…”

A Note on the Generalized Nonlinear Vector Variational-Like Inequality Problem

“…After that, this problem has been generalized and extended in various directions under different set-ups using different techniques. Liu et al [6], Zhao et al [7], and Ahmad and Irfan [8] are a few, who extended Browder's results to more generalized nonlinear variational inequalities. In 2009, Farajzadeh et al [9] considered new kinds of generalized variational-like inequality problems under the frame work of topological vector spaces.…”