• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.375-382
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• 2009

Several common stationary point theorems for two classes of contractive type multivalued mappings in a complete bounded metric space are given. The results presented in this paper generalize and extend some known results in literature.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.17-27
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• 2009

In the present work, we introduce two types of compatible maps and prove a common fixed point theorem for such maps in Menger probabilistic metric spaces. Our result generalizes and extends many known results in metric spaces and fuzzy metric spaces.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.777-798
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• 2018

In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.603-620
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• 2022

Several common fixed point theorems for a pair of weakly compatible mappings satisfying contractive inequalities of integral type in a metric space are proved. The results obtained in this paper improve or differ from a few results existing in the literature.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.1-17
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• 2004

In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.38-43
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• 2011

In this paper, we give definitions of compatible mappings of type(${\gamma}$) in intuitionistic fuzzy metric space and obtain common fixed point theorem under the conditions of weak compatible mappings of type(${\gamma}$) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by Sedghi et.al.[12].

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.643-649
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• 2013

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a strict mixed g-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.591-603
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• 2008

We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result.