• Nonlinear Functional Analysis and Applications
• /
• 제27권2호
• /
• pp.261-269
• /
• 2022

The purpose of this paper is to introduce a new generalization class of cyclic mappings, called cyclic generalized 𝜑-weak contraction and obtain a corresponding best proximity point theorem for this cyclic mapping under certain conditions.

• Nonlinear Functional Analysis and Applications
• /
• 제28권2호
• /
• pp.557-570
• /
• 2023

The conceptions of generalized b-metric spaces or G_b-metric spaces and a generalized Ω-distance mappings play a key role in proving many important theorems in existence and uniqueness of fixed point theory. In this manuscript, we establish a new type of contraction namely, Ω_b(𝓗, 𝜃, s)-contraction, this contraction based on the concept of a generalized Ω-distance mappings which established by Abodayeh et.al. in 2017 together with the concept of 𝓗-simulation functions which established by Bataihah et.al [10] in 2020. By utilizing this new notion we prove new results in existence and uniqueness of fixed point. On the other hand, examples and application were established to show the importance of our results.

• East Asian mathematical journal
• /
• 제32권3호
• /
• pp.333-354
• /
• 2016

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권1호
• /
• pp.23-38
• /
• 2014

In this paper, we introduce the concept of w¡compatibility and weakly commutativity for hybrid pair of mappings $F:X{\times}X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$ and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권1호
• /
• pp.35-51
• /
• 2016

We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X² → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

• East Asian mathematical journal
• /
• 제31권1호
• /
• pp.77-89
• /
• 2015

We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under generalized non-linear contraction. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

• Nonlinear Functional Analysis and Applications
• /
• 제27권3호
• /
• pp.587-601
• /
• 2022

In this article, we introduce the concept of contractive mapping, which is generally weak in metric spaces, and show the existence and uniqueness of the fixed point for such mapping in a metric space.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권1호
• /
• pp.73-96
• /
• 2016

We establish a coupled coincidence point theorem for generalized com-patible pair of mappings under generalized nonlinear contraction on a partially or-dered metric space. We also deduce certain coupled fixed point results without mixed monotone property of F : X × X → X . An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

• Nonlinear Functional Analysis and Applications
• /
• 제26권1호
• /
• pp.177-195
• /
• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• Nonlinear Functional Analysis and Applications
• /
• 제28권1호
• /
• pp.107-121
• /
• 2023

In this work, we study generalized integral type F-contractions in partial metric spaces and establish some common fixed point theorems. Also, we give some consequences of the established result. Our results extend and generalize several results from the existing literature.