• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.69-83
• /
• 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
• /
• v.37 no.4
• /
• pp.595-608
• /
• 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
• /
• v.24 no.1
• /
• pp.97-103
• /
• 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
• /
• v.29 no.1
• /
• pp.195-204
• /
• 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)).

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

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

• Korean Journal of Mathematics
• /
• v.30 no.2
• /
• pp.297-304
• /
• 2022

Fixed point theory has many useful applications in applied sciences. The object of this paper is to obtain fixed point for continuous self mappings in Hilbert C^*-module with rational conditions.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.2
• /
• pp.341-347
• /
• 2012

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending our work on Reidemeister orbit sets, we improve our theorem for formulae for Nielsen type essential orbit numbers.

• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.629-643
• /
• 2019

In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.

• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.369-375
• /
• 2008

In this paper, we first introduce inwards set valued maps in hyperconvex metric spaces. Then we present fixed point theory for continuous condensing inward set valued maps.