設X是一個非空G-凸空間，Y是一個拓樸空間，F屬於G-KKM(X,Y)，ψφ:X×Y→R 為二實值函數。在一些假設條件之下，我們證得一些推廣型的變分不等式。我們也證明了四個實值函數，在某些假設條件之下的一些大中取小不等式的存在性定理。本文的結果推廣了許多學者的研究結果。(特殊符號無法顯現請參閱PDF檔)

Let X be a nonempty G-convex space, let Y be a topological space, let F be G-KKM(X,Y), and let ψ,φ:X×Y→R be two real-valued mappings. In this paper, we establish some generalized variational inequality theorems under some assumptions. We also establish some minimax inequality theorems concerning four real-valued mappings under some assumptions. Our results generalize many other authors’ results.(特殊符號無法顯現請參閱PDF檔)

1. INTRODUCTION---------------------------------------5
2. PRELIMINARIES--------------------------------------6
3. MAIN RESULTS---------------------------------------10
4. REFERENCES-----------------------------------------17

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