• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.247-263
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• 2009

In this paper we use degree and index theory to present new applicable fixed point theory for permissible maps.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.69-83
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• 2009

New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

• 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.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• East Asian mathematical journal
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• v.24 no.1
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• pp.97-103
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• 2008

New fixed point theorems for permissible maps between $Fr{\acute{e}}chet$ spaces are presented. The proof relies on index theory developed by Dzedzej and on viewing a $Fr{\acute{e}}chet$ space as the projective limit of a sequence of Banach spaces.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.693-708
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• 2002

We generalize algebraic results of Nielsen fixed point theory to Nielsen coincidence theory. We use the algebraic methods of D. Ferrario in Nielsen fixed point theory.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.195-204
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• 2014

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).

• East Asian mathematical journal
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• v.24 no.3
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• pp.233-249
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• 2008

We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss $M{\ddot{o}}nch$ Kakutani and contractive type maps.

• 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.

• East Asian mathematical journal
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• v.24 no.1
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• pp.11-20
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• 2008

We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class $\cal{B}$ of maps. We also give 16 conjectures related to that theory.