這篇論文主要在探討透過非緊緻測度滿足F(ψ,ξ)函數在KKM性質下之定點
理論，文章前半段先討論KKM與測度的定義，接續著介紹定點的概念，進而討
論透過改變空間和連續性或是緊緻與否來測試，最後再由定義得出結論，並且
於第三部分提出應用。

This article is mainly to explore the fixed point results for the F(ψ,ξ)-contraction having KKM property via measure of noncompactness. First we talk about KKM property and measure of noncompactness and then introduce the Fixed point. Then discuss it is correct or not after we change the property，and we obtain the conclusion. Moreover, we have an application in the third part.

Contents
中文摘要......I
Abstract......II
Acknowledgement ......III
1.Introduction and preliminaries......1
2.Main results......5
3.Applications: The abstract variational inequality theroems......10
References......13

[1] A. Amini, M. Fakhar, J. Zafarni, KKM mappings in metric spaces, Nonlinear Anal., 60 (2005) 1045V1052.
[2] A.H. Ansari, Note on (ψ,φ)-contractive type mappings and related fixed point. In: The 2nd Regiobal Conference on Mathematics and Application, PNU, September 2014,, (2014) 377-380.
[3] S. Banach, Sur les operations dans les ensembles absraites et leurs applications, Fund. Math., 3 (1926) ,133-181
[4] T.H. Chang, C.L. Yen, KKM property and fixed point theorems, J. Math.
Anal. Appl., 203, (1996) 224–235.
[5] C.M Chen, Fixed point theorems for a k-set contraction in a metric space, Applied Mathematics Letters, 22,(2009) 101V104.
[6] C.M Chen, Tong-Huei Chang, Fixed Point Theorems for a weaker Meir-
Keeler Type ψ-Set Contraction in Metric Spaces, Fixed Point Theory and Appl., ,(2009) Article ID 129124.
[7] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat.Univ. Padova, 24 (1955) , 84-92.
[8] W.-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology and Applications, 159(2012), 49–56.
[9] B. Knaster, C. Kuratowski, S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale Simplexe, Fund. Math., 14 (1929) 132V137.
[10] Ky Fan, A generalization of Tychonoffs fixed point theorem, C.Math. Ann., 142 (1961) 305V310.
[11] A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28(1969), 326-329.
[12] N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., 141(1989),177V188.
[13] R. Nussbaum, The fixed point index and fixed point theorems for k-set contractions, Doctoral Dissertation, University of Chicago, 1969.
[14] M.S. Khan, M. Swaleh, S. Sessa,: Fixed point theorem by altering distances between the points, Bull. Aust. Math. Soc., 30(1)1984, 1-9.
[15] Farzazneh Nikbakhtsarvestani, S Mansour Vaezpour, Mehdi Asadi, F(ψ,φ)-contraction in terms of measure on noncompactness with application for nonlinear integral equations, J. Inequalities and Applications(2017), 271.
[16] P.M. Fitzpatrick, W.V. Petryshyn, Fixed point theorems for multivalued noncompact inward mappings, J. Math. Anal. Appl.64(1974), 756-767.