• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.399-410
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• 2012

We prove common fixed point theorems for weakly compatible mappings satisfying strict contractive conditions in fuzzy metric spaces using property (E.A). Our theorems extend a theorem of [1].

• The Journal of Fisheries Business Administration
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• v.34 no.1
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• pp.9-30
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• 2003

This paper tries to suggest a rational proposal for the distribution of compensation of common property fisheries damages caused by a large scale coastal reclamation. For the purpose the paper introduces the approach of alternative cost of the use of fishing ground. The background of the paper is the legal conflict between tenants and non-tenants, both of whom are common owners of seaweed cultivation ground, in the distribution of compensation for damages. In principal, so far as the seaweed cultivation right is a common property of the fishing association, the compensation is also a common property of it. Therefore the distribution method of the compensation entirely depends on the decision of the association. But in case that the numbers of non-tenants is larger than those of tenants, the distribution of the compensation is usually unfavorable to the tenants even though the latter is the key contributor to the realization of present value of the common property. The paper aims to show an appropriate distribution method based on the economic principle of optimal distribution. In others words, the value added to the economic value of alternative use of the fishing ground should be distributed to the tenants. the value amount of alternative use of the fishing ground should be equally distributed to the members of the association.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.127-138
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• 2015

The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying $\phi$-contractive condition.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.255-260
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• 2011

In this paper, we define the intuitionistic fuzzy contraction, and obtain some fixed point theorem using common property(E.A.) and weakly compatibility in intuitionistic fuzzy metric space.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.789-807
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• 2015

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

• Korean Journal of Mathematics
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• v.32 no.3
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• pp.561-591
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• 2024

In this article, we demonstrate the conditions for the existence of common fixed points (CFP) theorems for four self-maps satisfying the common limit range (CLR)-property on cone b-normed spaces (CbNS) via ℭ-class functions. Furthermore, we have a unique common fixed point for two weakly compatible (WC) pairings. Towards the end, the existence and uniqueness of common solutions for systems of functional equations arising in dynamic programming are discussed as an application of our main result.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.131-143
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• 2016

In this paper, we present some common fixed point theorems for two pairs of weakly compatible self-mappings on multiplicative metric spaces satisfying a generalized Meir-Keeler type contractive condition. The results obtained in this paper extend, improve and generalize some well known comparable results in literature.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.115-126
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• 2017

In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.467-475
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• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1839-1854
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• 2015

Brief developments in metrical fixed point theory are covered and a significant generalization of recent results obtained in [18], [27], [32] and [33] is established through an extension of the property (EA) to two sequences of self-maps using the notions of weak compatibility and implicit relation.