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Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation

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  • Gopal, Dhananjay
  • Abbas, Mujahid
  • Vetro, Calogero

Abstract

We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an α-ψ-type contractive mapping and then for a generalized β-type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results.

Suggested Citation

  • Gopal, Dhananjay & Abbas, Mujahid & Vetro, Calogero, 2014. "Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 955-967.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:955-967
    DOI: 10.1016/j.amc.2014.01.135
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    References listed on IDEAS

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    1. Choudhury, Binayak S. & Das, Krishnapada, 2009. "A coincidence point result in Menger spaces using a control function," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3058-3063.
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    Cited by:

    1. Rale M. Nikolić & Rajandra P. Pant & Vladimir T. Ristić & Aleksandar Šebeković, 2022. "Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    2. Badshah-e-Rome & Muhammad Sarwar & Rosana Rodríguez-López, 2021. "Fixed Point Results via α -Admissibility in Extended Fuzzy Rectangular b -Metric Spaces with Applications to Integral Equations," Mathematics, MDPI, vol. 9(16), pages 1-18, August.

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