• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.813-823
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• 2013

In this paper, a new iterative algorithm involving quasi-nonexpansive mapping in Hilbert space is proposed and proved to be strongly convergent to a point which is simultaneously a fixed point of a quasi-nonexpansive mapping, a solution of an equilibrium problem and the set of solutions of a variational inequality problem. The results of the paper extend previous results, see, for instance, Takahashi and Takahashi (J Math Anal Appl 331:506-515, 2007), P.E.Maing $\acute{e}$ (Computers and Mathematics with Applications, 59: 74-79,2010) and other results in this field.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.257-267
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• 2021

In this paper, we develop an iterative algorithm for obtaining common solutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.61-74
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• 2011

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming and the descent-like method for finding a common element of the solution set for a variational inequality and the set of common fixed points of a nonexpansive semigroup in Hilbert spaces. We obtain a strong convergence for the sequence generated by our method in Hilbert spaces. The result in this paper modifies and improves some well-known results in the literature for a more general problem.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.25-35
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• 2008

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials that share fixed-points. Moreover we extend former results of W. C. Lin and H. X. Yi.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.161-173
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• 2009

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.69-82
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• 2010

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an asymptotically k-strict pseudo-contractive mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results are more general than the known results which are given by many authors. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.55-60
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• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.725-742
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• 1996

In this paper we give some sharp expressions of the weakly convergent sequence coefficient WCS(X) of a Banach space X. They are used to prove fixed point theorems for involution mappings T from a weakly compact convex subset C of a Banach space X with WCS(X) > 1 into itself which $T^2$ are both of asymptotically nonexpansive type and weakly asymptotically regular on C. We also show that if X satisfies the semi-Opial property, then every nonexpansive mapping $T : C \to C$ has a fixed point. Further, some questions for asymtotically nonexpansive mappings are raised.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.83-98
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• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results