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Proceedings of Fifth International Conference on Soft Computing for Problem Solving pp 65–70Cite as

Common Fixed-Point Theorem for Set-Valued Occasionally Weakly Compatible Mappings in Fuzzy Metric Spaces

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 437))

Abstract

In our paper, we prove common fixed-point theorem on the basis of control functions in FM-spaces. Using the fuzzy edition of the Banach contraction principle, the present theorem generalized the Banach contraction principle using the continuous control function. Condition of continuity for mappings \(P,Q,S\) and \(T\) is not required. Our result generalizes the accumulation of compact subsets of \(Y,\) where the assemblage \(H_{M}\) itself is an FM-space. Here, we prove the result for two pairs of single-valued and set-valued owc mappings. Also, we give example to justify our result.

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Author information

Authors and Affiliations

  1. M. M. University Mullana, Ambala, Haryana, India

    Vishal Gupta & Manu Verma

  2. Bundelkhand University, Jhansi, UP, India

    R. K. Saini

Authors
  1. Vishal Gupta
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  2. R. K. Saini
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  3. Manu Verma
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Corresponding author

Correspondence to Vishal Gupta .

Editor information

Editors and Affiliations

  1. Dept of Applied Sci & Eng, Indian Instit of Tech Roorkee, Roorkee, India

    Millie Pant

  2. Department of Mathematics, Indian Inst of Tech Roorkee, Roorkee, India

    Kusum Deep

  3. Dept of Mathematics, South Asian University New Delhi, New Delhi, India

    Jagdish Chand Bansal

  4. Department of Mathematics and Comp Sci, Liverpool Hope University, LIVERPOOL, United Kingdom

    Atulya Nagar

  5. Department of Mathematics, National Inst of Tech Silchar, Silchar, Assam, India

    Kedar Nath Das

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© 2016 Springer Science+Business Media Singapore

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Gupta, V., Saini, R.K., Verma, M. (2016). Common Fixed-Point Theorem for Set-Valued Occasionally Weakly Compatible Mappings in Fuzzy Metric Spaces. In: Pant, M., Deep, K., Bansal, J., Nagar, A., Das, K. (eds) Proceedings of Fifth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 437. Springer, Singapore. https://doi.org/10.1007/978-981-10-0451-3_7

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  • DOI: https://doi.org/10.1007/978-981-10-0451-3_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0450-6

  • Online ISBN: 978-981-10-0451-3

  • eBook Packages: EngineeringEngineering (R0)

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