• East Asian mathematical journal
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• v.31 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.575-585
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• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.

• East Asian mathematical journal
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• v.18 no.1
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• pp.127-136
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• 2002

In this paper we obtain some fixed points theorems of expansive mappings and several necessary and sufficient conditions for the existence of common fixed points of families of self-mappings in metric spaces. Our results generalize and improve the main results of Fisher [1]-[5], Furi-Vignoli [6], $Is\'{e}ki$ [7], Jungck [8], [9], Kashara-Rhoades [10], Liu [13], [14] and Sharma and Strivastava [16].

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1037-1056
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• 2016

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

• The Mathematical Education
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• v.23 no.2
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• pp.55-59
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• 1985

In this paper we obtain several results on the existence of common fixed points, of commuting mappings on PM-spaces and give an application. Our results generalize a multitude of fixed point theorems in PM-spaces.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.785-791
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• 2008

In this paper, we give a generalized contractive type condition for a pair of self maps of a metric space and analyze the existence of common fixed points for these maps of a metric space.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.577-581
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• 2003

Some random fixed point theorems for weakly inward multivalued random maps are obtained in Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.33-39
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• 2005

In this paper, we prove the existence of a common random fixed point of two random multivalued generalized contractions by using functional expressions.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.113-120
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• 2001

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

• East Asian mathematical journal
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• v.39 no.1
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• pp.1-10
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• 2023

In this paper, we introduce two kinds of implicit conditions and establish some fixed point theorems in cone S-metric spaces, which generalize the several existing results.