About Applications of the Fixed Point Theory

Author:

Bucur Amelia1

Affiliation:

1. “Lucian Blaga” University of Sibiu , Sibiu , Romania

Abstract

Abstract The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

Publisher

Walter de Gruyter GmbH

Reference18 articles.

1. Alfuraidan, M., & Ansari, Q. (2016). Fixed point theory and graph theory: Foundations and integrative approaches, London, England: Academic Press-Elsevier.

2. Guran, L., & Bota, M.-F. (2015). Ulam-Hyers stability problems for fixed point theorems concerning α-ψ-Type contractive operators on KST-Spaces, International Conference on Nonlinear Operators, Differential Equations and Applications, Cluj-Napoca, Romania.

3. Hasanzade Asl, J., Rezapour, S., & Shahzad, N. (2012). On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory and Applications, 212. doi: 10.1186/1687-1812-2012-212.

4. Isac, G., Yuan, X.-Z., Tan, K. K., & Yu, I. (1998). The study of minimax inequalities, abstract economics and applications to variational inequalities and nash equilibria, Acta Appl. Math., 54(2), 135-166.

5. Kohlberg, E., & Mertens, J. F. (1986). On the strategic stability of equilibrium points, Econometrica, 54, 1003-1037.

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