Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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SOME BEST PROXIMITY POINT RESULTS OF SEVERAL 𝛼-𝜓 INTERPOLATIVE PROXIMAL CONTRACTIONS

  • Deng, Jia (College of Mathematics and Statistics, Sichuan University of Science and Engineering) ;
  • Liu, Xiao-lan (College of Mathematics and Statistics, Sichuan University of Science and Engineering, South Sichuan Center for Applied Mathematics) ;
  • Sun, Yan (College of Mathematics and Statistics, Sichuan University of Science and Engineering) ;
  • Rathour, Laxmi
  • Received : 2021.04.28
  • Accepted : 2022.04.27
  • Published : 2022.09.01
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Abstract

In this paper, we introduce several types 𝛼-𝜓 interpolative proximal contractions and provide some sufficient conditions to prove the existence of best proximity points for these contractions in metric spaces. In the case of proximal contraction of the first kind, these metric spaces are not necessarily complete. Meanwhile, some new results can derive from our results. Finally, some examples are provided to show the validity of our results.

Keywords

Acknowledgement

This work is partially supported by National Natural Science Foundation of China (Grant No.11872043), Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province (Grant No.2021ZYD0017), Zigong Science and Technology Program (Grant No.2020YGJC03), 2021 Innovation and Entrepreneurship Training Program for College Students of Sichuan University of Science and Engineering (Grant No.cx2021150).

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