Fixed Point and Endpoint Theorems for $(\alpha,\beta)$-Meir-Keeler Contraction on the Partial Hausdorff Metric

Komi Afassinou, Ojen Kumar Narain

Abstract


The purpose of this work is to introduce the notion of a multi-value strictly $(\alpha,\beta)$-admissible mappings and a multi-value $(\alpha,\beta)$-Meir-Keeler contraction with respect to the partial Hausdorff metric $\mathcal{H}_{p}$ in the framework of partial metric spaces. In addition, we present fixed points and endpoints results for a multi-valued $(\alpha,\beta)$-Meir-Keeler contraction mappings in the framework of the complete partial metric spaces. The results obtained in this work provides extension as well as substantial generalizations and improvements of several well-known results on fixed point theory and its applications.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|