Xinhong Chen¹, Wenxiang Han², Liping Gong³, Chengjun Luo³

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¹ College of Science, Zhongyuan University of Technology, Zhengzhou, China.
² School of Civil Engineering, Zhongyuan University of Technology, Zhengzhou, China.
³ School of Foreign Languages, Zhongyuan University of Technology, Zhengzhou, China.
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Abstract: In this paper, we suggest and analyze a modified Thakur three-step iterative algorithm to approximate a common element of the set of common fixed points of Garcia-Falset mappings and the set of solutions of some variational inequalities in Banach spaces. We also establish strong convergence theorems for a common solution of the above-said problems by the proposed iterative algorithm without the compactness assumption. The methods in this paper are novel and different from those given in many other papers. And the results are the extension and improvement of the recent results announced by many others.

Keywords: Banach Space, Fixed Point, Garcia-Falset Mapping, Strong Convergence, Variational Inequality

Cite this paper: Chen, X. , Han, W. , Gong, L. and Luo, C. (2020) A Modified Thakur Three-Step Iterative Algorithm to Garcia-Falset Mappings and Variational Inequalities. Journal of Applied Mathematics and Physics, 8, 2930-2942. doi: 10.4236/jamp.2020.812216.

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