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Finding a Solution to an Optimization Problem and an Application

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Abstract

In this paper, we obtain some best proximity point results on 0-complete partial metric spaces by introducing a new concept of mixed multivalued contraction mapping. Thus, we generalize and extend some important and famous results existing in the literature. To support our results, we present a noteworthy illustrative and comparative example. Finally, we give some applications of our new best proximity point theorems to homotopy theory as directly unlike homotopy applications existing in the literature. Hence, we prove some best proximity point results for homotopic mappings.

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Acknowledgements

The author is thankful to the referees for making valuable suggestions leading to the better presentations of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Çankırı Karatekin University, 18100, Çankırı, Turkey

    Mustafa Aslantas

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  1. Mustafa Aslantas
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Correspondence to Mustafa Aslantas.

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Communicated by Sándor Zoltán Németh.

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Aslantas, M. Finding a Solution to an Optimization Problem and an Application. J Optim Theory Appl 194, 121–141 (2022). https://doi.org/10.1007/s10957-022-02011-4

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