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Finding a Solution to an Optimization Problem and an Application

Author

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  • Mustafa Aslantas

    (Çankırı Karatekin University)

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.

Suggested Citation

  • Mustafa Aslantas, 2022. "Finding a Solution to an Optimization Problem and an Application," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 121-141, July.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02011-4
    DOI: 10.1007/s10957-022-02011-4
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    References listed on IDEAS

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    1. Abdul Latif & Talat Nazir & Mujahid Abbas, 2019. "Fixed Point Results for Multivalued Prešić Type Weakly Contractive Mappings," Mathematics, MDPI, vol. 7(7), pages 1-14, July.
    2. Ali Abkar & Moosa Gabeleh, 2013. "Best proximity points of non-self mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 287-295, July.
    Full references (including those not matched with items on IDEAS)

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