• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.643-649
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• 2013

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a strict mixed g-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.455-466
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• 2021

Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in G-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.

• Kyungpook Mathematical Journal
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• 제54권3호
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• pp.485-500
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• 2014

In this paper, we establish coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving a pair of altering distance functions in ordered G-metric spaces. Via presented theorems we extend and generalize the results of Harjani et al. [J. Harjani, B. L$\acute{o}$pez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011) 1749-1760] and Choudhury and Maity [B.S. Choudhury and P. Maity, Coupled fixed point results in generalized metric spaces. Math. Comput. Model. 54 (2011), 73-79].

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.441-453
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• 2021

In this work, we define the concept of a mixed G-monotone mapping on a modular metric space endowed with a graph, and prove some fixed point theorems for this new class of mappings. Results of this paper extend coupled fixed point theorems from partially ordered metric spaces into the modular metric spaces endowed with a graph. An example is presented to illustrate the new result.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.1-11
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• 2019

In this paper we prove certain coupled coincidence point and coupled common fixed point results in partially ordered metric spaces for a pair of compatible mappings which satisfy certain rational inequality. The results are supported with two examples.

• East Asian mathematical journal
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• 제31권1호
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• pp.65-75
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• 2015

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

• East Asian mathematical journal
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• 제32권5호
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• pp.745-765
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• 2016

We propose coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. In particular, it is shown that the results existing in the literature are extend, generalized, unify and improved by using mixed monotone property. Given to support the useability of our results, and to distinguish them from the known ones.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.159-180
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• 2013

We establish a common fixed point theorem for mappings under ${\phi}$-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.559-580
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• 2024

In this paper, we aim to prove coupled and common coupled fixed point theorems for contractive type conditions in the context of partial metric spaces by means of a control function, and to provide some corollaries of the established results. This paper presents a number of results that generalize and extend previous work in the field. In order to better illustrate the process, we provide examples.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.73-94
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• 2018

We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.