4.7 Article

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

期刊

MATHEMATICS
卷 9, 期 23, 页码 -

出版社

MDPI
DOI: 10.3390/math9233001

关键词

fuzzy metric space; fixed point; Proinov-type contraction; non-Archimedean fuzzy metric space

资金

  1. National Natural Science Foundation of China [11872043]
  2. Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Internationalization and Internet of Things [2020WYJ01]
  3. Sichuan Science and Technology Program [2019YJ0541]
  4. Scientific Research Project of Sichuan University of Science and Engineering [2017RCL54, 2019RC42, 2019RC08]
  5. Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing [2019QZJ03]
  6. Open Fund Project of Artificial Intelligence Key Laboratory of Sichuan Province [2018RYJ02]
  7. Zigong Science and Technology Program [2020YGJC03]
  8. Graduate Innovation Project of Sichuan University of Science and Engineering [y2020078]
  9. Project of Ministerio de Ciencia e Innovacion [PID2020-119478GB-I00]
  10. Junta de Andalucia of the Andalusian PAIDI [FQM-365]
  11. Program FEDER Andalucia 2014-2020 [A-FQM-170-UGR20]

向作者/读者索取更多资源

This study introduces a new family of fuzzy contractions based on Proinov-type contractions, with very weak constraints on the auxiliary functions, proving the existence and uniqueness of fixed points and addressing some open problems.
Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form psi(d(Tx,Ty))& LE;phi(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldan Lopez de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

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