Journal of Guangxi Normal University(Natural Science Edition) ›› 2019, Vol. 37 ›› Issue (4): 79-85.doi: 10.16088/j.issn.1001-6600.2019.04.010

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The Existence of Solutions for Quasi-variational Inequalities by Using the Fixed Point Index Approach

ZHU Yaping1, QU Guorong2, FAN Jianghua1*   

  1. 1.College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China;
    2.Department of Basic Education, Guilin Tourism University, Guilin Guangxi 541006, China
  • Received:2019-01-13 Online:2019-10-25 Published:2019-11-28

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Abstract: A class of generalized projection operator is defined in this paper, and some properties of the generalized projection operator are obtained in reflexive, locally uniformly convex,smooth Banach spaces. The equivalence between the quasi-variational inequality problem and the fixed point problem is established. A concept of fixed point index of quasi-variational inequality is introduced and the fixed point index approach is applied to obtain the existence results for solutions of quasi-variational inequality problem under some conditions.

Key words: quasi-variational inequality, existence of solution, generalized projection operator, fixed point index

CLC Number: 

  • O177.91
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