• Honam Mathematical Journal
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• v.22 no.1
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• pp.91-97
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• 2000

In this paper we obtain a criterion for the existence of a common fixed point of a pair of mappings in 2-metric spaces. Our result generalizes a number of fixed point theorems given by Imdad, Khan and Khan [1], Kahn and Fisher [2], Kubiak [3], Rhoades [5], and Singh, Tiwari and Gupta [6].

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.617-631
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• 2012

In this paper, we will consider some existence theorems of common fixed points for a countable family of non-self multi-valued mappings defined on a closed subset of a complete metrically convex space, and give more generalized common fixed point theorems for a countable family of single-valued mappings. The main results in this paper generalize and improve many common fixed point theorems for single valued or multi-valued mappings with contractive type conditions.

• East Asian mathematical journal
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• v.25 no.1
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• pp.1-10
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• 2009

In this paper, we prove some common fixed point theorems of compatible mappings under the generalized contractive type in metric spaces and also give some examples to illustrate our main theorems. This results extend the results of several authors.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.103-111
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• 2014

Let X be a uniformly convex Banach space, and S, T be pair of mean nonexpansive mappings. Some necessary and sufficient conditions are given for Ishikawa iterative sequence converge to common fixed points, and we prove that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T. This generalizes former results proved by Z. Gu and Y. Li [4].

• 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].

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.607-614
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• 2008

We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.2
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• pp.147-153
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• 2013

Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(${\beta}$) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(${\beta}$) in an intuitionistic fuzzy metric space. This paper also presents an example of a common fixed point that satisfies the conditions of Theorem 4.1 in an intuitionistic fuzzy metric space.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.13-28
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• 2015

In this paper, we use two mappings satisfying certain expansive conditions to construct convergent sequences in complex valued metric spaces, and then we prove that the limits of the convergent sequences are the points of coincidence or common fixed points for the two mappings. The main theorems in this paper are the generalizations and improvements of the corresponding results in real metric spaces, cone metric spaces and topological vector space-valued cone metric spaces.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.161-174
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• 2017

The objective of this manuscript is to continue the study of fixed point theory in dislocated metric spaces, introduced by Hitzler et al. [12]. Concretely, we apply the concept of dislocated metric spaces and obtain theorems asserting the existence of common fixed points for a pair of mappings satisfying new generalized rational contractions in such spaces.