• Honam Mathematical Journal
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• v.37 no.4
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• pp.595-608
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• 2015

In this paper, as a survey paper, we review many works related to fixed point theory for digital spaces using Lefschetz fixed point theorem, Banach fixed point theorem, Nielsen fixed point theorem and so forth. Besides, we refer some properties of the fixed point property of a digital k-retract.

• East Asian mathematical journal
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• v.27 no.5
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• pp.573-583
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• 2011

In this paper, we prove a common fixed point theorem for noncompatible, discontinuous mappings on a Banach space. Our main theorem extends, improves, generalizes some known results on Banach spaces.

• East Asian mathematical journal
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• v.17 no.1
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• pp.33-45
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• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.269-287
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• 2021

In this paper, we prove some coupled fixed point theorems satisfying some generalized contractive condition in a cone metric space over a Banach algebra. We also applied the results obtained to show coupled fixed point of some contractive mapping of integral type.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.401-408
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• 2006

Fixed point theory is one of famous theories from theoretical and numerical point of views. Banach fixed point theorem plays a main role in this theory. In this article, Grabiec's fuzzy Banach contraction theorem [3] and Vasuki's theorem [12] for a complete fuzzy metric space, in the sense of Song [11] (or George and Veeramani), is proved by an extra condition.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.327-337
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• 2008

In this paper, we prove strong convergence theorems of Halpern iteration for relatively asymptotically nonexpansive mappings in the framework of Banach spaces. Our results extend and improve the recent ones announced by [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400-2411], [X. Qin, Y. Su, Strong convergence theorem for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965] and many others.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-13
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• 1999

Sufficient conditions for controllability of semilinear second order Volterra integrodifferential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.101-116
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• 2005

Using the iterative method, we derive an controller realization of the bilinear system, which is resulted from the system reformulation. We utilize Banach Fixed Point Theorem to support proposed controller, and the simulation results are also illustrated to verify usefulness of this technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.41-54
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• 2004

Sufficient conditions for the controllability of neutral functional integrodifferential systems with infinite delay in Banach space are established by means of the Schaefer fixed point theorem.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.283-287
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• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.