• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.883-892
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• 2023

In this research, under some specific situations, we precisely derive new coupled fixed point theorems in a complete b-metric space endowed with the graph. We also use the concept of coupled fixed points to ensure the solution of differential equations for the system of impulse effects.

• 한국소음진동공학회논문집
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• 제14권8호
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• pp.718-725
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• 2004

If a wall separates the bounded and unbounded spaces, then the wall’s role in transporting the acoustic characteristics of the two spaces is not well defined. In this paper, we attempted to see how the acoustic characteristics of two spaces are really affected by the spatial characteristics of the wall. In order to understand coupling mechanism, we choose a finite space and a semi-infinite space separated by the flexible or rigid wall and an opening. A volume interaction can be occurred in structure boundary and a pressure Interaction can be happened in the opening boundary. For its simplicity, without loosing generality, we use rather simplified rectangle model instead of generally shaped model. The source impedance is presented to the various types of boundaries. The distributions of pressure and active intensity are also presented at the cavity- and structure-dominated modes. The resulting modification, shifts of modal frequencies and changing of standing wave patterns to satisfy both coupled boundary conditions and governing equations, are presented.

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

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.289-307
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• 2023

We prove some common fixed point theorems for β-non-decreasing mappings under contraction mapping principle on partially ordered metric spaces. We study the existence of solution for periodic boundary value problems and also give an example to show the degree of validity of our hypothesis. Our results improve and generalize various known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권2호
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• pp.79-98
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• 2017

We establish a coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X{\times}X{\rightarrow}X$ under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of $F:X{\times}X{\rightarrow}X$. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

• 대한수학회보
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• 제50권3호
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• pp.993-1005
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• 2013

In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.

• 대한수학회논문집
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• 제5권2호
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• pp.87-111
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• 1990

• East Asian mathematical journal
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• 제32권3호
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• pp.333-354
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• 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
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• 제30권3호
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• pp.249-267
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• 2023

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.443-461
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• 2023

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.