Extended new generalized mixed vector variational-like inequalities in reflexive Banach spaces

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• 作者：P. Majee ; C. Nahak
• 关键词：Extended new generalized mixed vector variational ; like inequalities ; Relaxed semi ; α ; monotonicity ; Fan ; KKM theorem ; Nadler’s result ; Brouwer’s fixed point theorem
• 刊名：OPSEARCH
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：53
• 期：4
• 页码：934-949
• 全文大小：247 KB
• 刊物主题：Operations Research/Decision Theory; Management/Business for Professionals; Mathematics, general;
• 出版者：Springer India
• ISSN：0975-0320
• 卷排序：53

文摘

In this paper, we introduce and study an extended new generalized mixed vector variational-like inequality (ENGMVVLI) problem in real reflexive Banach spaces. This problem is more general than many existing equilibrium problems and variational inequalities available in the literature. We prove the existence results of (ENGMVVLI) by utilizing the KKM lemma and Nadlar’s results with relaxed semi- α-monotone mappings. Also, by using the Brouwer’s fixed point theorem, we prove the existence of solutions for (ENGMVVLI) without using the monotonicity concept. Finally, we give an example to justify the validity of our results.