• Korean Journal of Mathematics
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• 제23권3호
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• pp.409-425
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• 2015

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.715-723
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• 2009

The aim of this paper is to present an explicit iteration method for finding a common fixed point of a finite family of strictly pseudocon-tractive mappings defined on q-uniformly smooth and uniformly convex Banach spaces.

• 충청수학회지
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• 제33권4호
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• pp.387-394
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• 2020

Matthews introduced the concepts of partial metric spaces and proved the Banach fixed point theorem in complete partial metric spaces. Dukic, Kadelburg, and Radenovic proved fixed point theorems for Geraghty-type mappings in complete partial metric spaces. In this paper, we prove the fixed point theorem for some contractive mapping in a complete partial metric space.

• 충청수학회지
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• 제23권4호
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• pp.599-608
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• 2010

In this paper, we introduce the concept of generalized weak contractivity for set-valued maps defined on quasi metric spaces. We analyze the existence of fixed points for generalized weakly contractive set-valued maps. And we have Nadler's fixed point theorem and Banach's fixed point theorem in quasi metric spaces. We investigate the convergene of iterate schem of the form $x_{n+1}{\in}Fx_n$ with error estimates.

• 대한수학회보
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• 제36권3호
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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 the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.67-75
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• 2000

Sufficient conditions for boundary controllability of time varying delay integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.149-156
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• 2001

Sufficient conditions for boundary controllability of semilinear systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Banach contraction principle. An example is provided to illustrate the theory.

• 대한수학회보
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• 제21권2호
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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.

• 대한수학회논문집
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• 제11권3호
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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.

• 대한수학회논문집
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• 제25권4호
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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.