本文關(guān)鍵詞： 變分不等式 廣義松弛擬單調(diào)算子 廣義松弛擬凸函數(shù) 平衡問題 廣義松弛上半點性質(zhì)　出處：《四川師范大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：本文在賦范空間中研究了集值映射的一種新的單調(diào)性,稱之為廣義松弛擬單調(diào)映射.運用KKM理論,在新引入的單調(diào)映射下我們證明了變分不等式的解集非空.同時,討論了廣義松弛擬凸函數(shù)與廣義松弛擬單調(diào)映射之間的關(guān)系.此外,本文給出了當(dāng)廣義松弛擬單調(diào)映射具有廣義松弛上半點性質(zhì)時,對偶平衡問題解集非空,從而獲得平衡問題解集非空.
[Abstract]:In this paper, we study a new monotonicity of set-valued mappings in normed spaces, which is called generalized relaxed quasi-monotone mappings. Using KKM's theory, we prove that the solutions of variational inequalities are nonempty under the newly introduced monotone mappings. The relationship between generalized relaxed quasiconvex functions and generalized relaxed quasi-monotone mappings is discussed. In addition, when generalized relaxed quasi-monotone mappings have the property of generalized relaxation upper half point, the solutions of dual equilibrium problems are not empty. Thus, the solution set of the equilibrium problem is not empty.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O178
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本文編號：1503823