Some coupled coincidence point results in partially ordered metric spaces

Fadakar, Laya; Işık, Huseyin; Tavakoli, Shirin; Mardzad, Arezo

doi:10.30495/maca.2021.1929674.1010

Some coupled coincidence point results in partially ordered metric spaces

https://doi.org/10.30495/maca.2021.1929674.1010

Volume 3, Issue 2
Spring 2021

Pages 40-54

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Laya Fadakar ¹

Huseyin Işık ²

Shirin Tavakoli ¹

Arezo Mardzad ¹

¹ Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran

² Department of Engineering Science, Bandırma Onyedi Eylul University, 10200, Bandırma, Balıkesir, Turkey

Abstract

In this paper, we introduce the notion of partial-compatibility of mappings in an ordered partial metric space and use this notion to establish coupled coincidence point theorems for $\phi$-mixed monotone mappings satisfying a nonlinear contraction condition. Our consequences is an extension of the results of Shatanawi et al. [W. Shatanawi, B. Samet and M. Abbas, \textit{Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces}, Math. Comp. Model., 55(3-4) (2012), 680-687]. We also provide an example to illustrate the results
presented herein.

Keywords

Coupled coincidence point

Partially ordered set

Partial metric space

Mixed monotone property

Compatible mapping

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