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Fixed-Point Theorems in Fuzzy Metric Spaces via Fuzzy F -Contraction

Author

Listed:
  • Huaping Huang

    (School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China)

  • Biljana Carić

    (Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia)

  • Tatjana Došenović

    (Faculty of Technology Novi Sad, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia)

  • Dušan Rakić

    (Faculty of Technology Novi Sad, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia)

  • Mirjana Brdar

    (Faculty of Technology Novi Sad, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia)

Abstract

The purpose of this paper is to introduce a new type of contraction called fuzzy F -contraction. As compared to the F -contraction in the existing literature, our fuzzy F -contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F -contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature.

Suggested Citation

  • Huaping Huang & Biljana Carić & Tatjana Došenović & Dušan Rakić & Mirjana Brdar, 2021. "Fixed-Point Theorems in Fuzzy Metric Spaces via Fuzzy F -Contraction," Mathematics, MDPI, vol. 9(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:641-:d:519029
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