• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.73-96
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• 2016

We establish a coupled coincidence point theorem for generalized com-patible pair of mappings under generalized nonlinear contraction on a partially or-dered metric space. We also deduce certain coupled fixed point results without mixed monotone property of F : X × X → X . An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.73-94
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• 2018

We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.

• 대한수학회지
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• 제38권3호
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• pp.669-681
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• 2001

This paper introduces the notions of essential and inessential map for countably $textsc{k}$-set contractive maps. These ideas enable us to establish a Krasnoselskii-Petryshyn compression and expansion theorem in a cone for countably $textsc{k}$-set contractive maps.

• 대한수학회지
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• 제52권6호
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• pp.1287-1303
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• 2015

The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.

• 대한수학회논문집
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• 제29권2호
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• pp.367-377
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• 2014

In this paper, we first introduce a generalized concept of Berge strong equilibrium for a generalized game $\mathcal{G}=(X_i;T_i,f_i)_{i{\in}I}$ of normal form, and using a fixed point theorem for compact acyclic maps in admissible convex sets, we establish the existence theorem of generalized Berge strong equilibrium for the game $\mathcal{G}$ with acyclic values. Also, we have demonstrated by examples that our new approach is useful to produce generalized Berge strong equilibria.

• 대한수학회논문집
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• 제24권4호
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• pp.523-528
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• 2009

In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• 대한수학회지
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• 제35권4호
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• pp.803-829
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• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• 대한수학회보
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• 제54권1호
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• pp.199-214
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• 2017

We consider fixed-point iterations constructed by simple transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.