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Darbo type best proximity point results via simulation function with application

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Abstract

Primarily this work intends to prove the best proximity point (pair) results using the concept of measure of noncompactness and simulation functions. The obtained results generalize and extend some present state of the art on Darbo type fixed point theorems. The main results are applied to actualize the optimum solutions of a system of nonlinear mixed Fredholm–Volterra functional integro-differential equations with local initial conditions.

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Acknowledgements

The authors thank the referees for useful comments and suggestions for the improvement of the paper. The second author is thankful for the support of NBHM, Department of Atomic Energy, Govt. of India (Grant No.-02011/27/2017/R&D-II/11630).

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Authors and Affiliations

  1. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India

    Pradip Ramesh Patle & Deepesh Kumar Patel

  2. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

    Reza Arab

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  1. Pradip Ramesh Patle
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  2. Deepesh Kumar Patel
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  3. Reza Arab
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Correspondence to Deepesh Kumar Patel.

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Patle, P.R., Patel, D.K. & Arab, R. Darbo type best proximity point results via simulation function with application. Afr. Mat. 31, 833–845 (2020). https://doi.org/10.1007/s13370-020-00764-7

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  • DOI: https://doi.org/10.1007/s13370-020-00764-7

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