• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.23-38
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• 2014

In this paper, we introduce the concept of w¡compatibility and weakly commutativity for hybrid pair of mappings $F:X{\times}X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$ and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.499-512
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• 2022

In this paper, we construct an iteration scheme involving a hybrid pair of the Suzuki generalized nonexpansive single-valued and multi-valued mappings in a complete CAT(0) space. In process, we remove a restricted condition (called end-point condition) in Akkasriworn and Sokhuma's results [2] in Banach spaces and utilize the same to prove some convergence theorems. The results in this paper, are analogs of the results of Akkasriworn et al. [3] in Banach spaces.

• 대한수학회보
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• 제46권5호
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• pp.885-894
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• 2009

In this paper, we consider a hybrid projection algorithm for a pair of inverse-strongly monotone mappings and a quasi-$\phi4-nonexpansive mapping. Strong convergence theorems are established in the framework of Banach spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.59-82
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• 2022

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

• 충청수학회지
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• 제23권4호
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• pp.801-812
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• 2010

In this paper, we consider the convergence of the shrinking projection method for quasi-$\phi$-nonexpansive mappings. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which enjoys the Kadec-Klee property.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.179-190
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• 2007

In this paper, we consider the general variational inequality GVI(F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type method $u_{n+l}=(1-{\alpha}+{\theta}_{n+1})Tu_n+{\alpha}u_n-{\theta}_{n+1g}(Tu_n)-{\lambda}_{n+1}{\mu}F(Tu_n),\;n{\geq}0$. for solving the general variational inequalities. The sequence $\{x_n}\$ is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.103-117
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• 2024

In this article, we utilize the concepts of hybrid rational Geraghty type generalized F-contraction and to prove some fixed point results for such mappings are in the perspective of partially ordered b-metric like space. Some innovative examples are also presented which substantiate the validity of obtained results. The example is also authenticated with the help of graphical representations.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.523-558
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• 2021

In this paper, we study some fixed point properties of n-generalized Bregman nonspreading mappings in reflexive Banach space. We introduce a hybrid iterative scheme for finding a common solution for a countable family of equilibrium problems and fixed point problems in reflexive Banach space. Further, we give some applications and numerical example to show the importance and demonstrate the performance of our algorithm. The results in this paper extend and generalize many related results in the literature.