• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.565-578
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• 1999

In this paper some common fixed point theorems for pairs of condensing mappings in a Banach space are proved and applications are given to a pair of nonlinear first order ordinary differential equations in Banach spaces for proving the existence of common solution under suitable conditions.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.61-73
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• 2008

In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.41-45
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• 1994

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.343-350
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• 2009

We prove the existence of common fixed point for multivalued maps satisfying general contractive type conditions.

• East Asian mathematical journal
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• v.18 no.2
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• pp.225-233
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• 2002

In this paper, we obtain the common fixed point for fuzzy mappings satisfying an implicit relation. We improve earlier results of this line.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.201-217
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• 2011

The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.411-424
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• 2006

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck's common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem ([21]).

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.483-498
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• 2011

In this paper, we introduce a new class of uniformly point-wise R-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly point-wise R-subweakly commuting asymptotically I-nonexpansive mappings in normed linear spaces. We also establish some results concerning strong convergence of nearest common fixed points of asymptotically I-non-expansive mappings in reflexive Banach spaces with a uniformly G$\^{a}$teaux differentiable norm. Our results unify and generalize various known results given by some authors to a more general class of noncommuting mappings.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.583-607
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• 2010

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

• 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.