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Some fixed point theorems for \(S_F\)-contraction in complete fuzzy metric spaces

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Abstract

In this paper, we prove some fixed point theorems by introducing a new F-contraction namely \(S_F\)-contraction in fuzzy metric spaces by combining the idea of Wardowski’s (Fixed Point Theory Appl 2012, Article ID 94, 2012) and Secelean’s (Fixed Point Theory Appl 2013, Article ID 277, 2013) contractions in metric spaces and Grabiec’s (Fuzzy Sets Syst 125, 385–389, 1988) contraction in fuzzy metric spaces. An example is also given to support the results proved herein.

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Acknowledgements

All the authors are thankful to the learned referees for their fruitful suggestions towards improvements of the paper. A. Sharma is thankful to National Board of Higher Mathematics (NBHM) for awarding Post Doctoral Fellowship.

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Authors and Affiliations

  1. Department of Mathematics, Chandigarh University, Gharuan, Mohali, 140413, India

    Surjeet Singh Chauhan

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Mohammad Imdad

  3. Punjab Technical University, Jalandhar, 144603, India

    Gurjeet Kaur

  4. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016, India

    Anupam Sharma

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  1. Surjeet Singh Chauhan
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  2. Mohammad Imdad
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  4. Anupam Sharma
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Correspondence to Anupam Sharma.

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Chauhan, S.S., Imdad, M., Kaur, G. et al. Some fixed point theorems for \(S_F\)-contraction in complete fuzzy metric spaces. Afr. Mat. 30, 651–662 (2019). https://doi.org/10.1007/s13370-019-00673-4

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