Coupled fixed points via simulation functions

Authors

Keywords:

Coupled fixed point; Simulation function; Functional-integral equation

Abstract

In the present paper, we show a result in complete metric spaces about the existence and uniqueness of coupled fixed points by using
simulation functions. Moreover, we illustrate our result presenting a theorem about the existence and uniqueness of solution to a general system of nonlinear functional-integral equations.

Author Biographies

  • Josefa Caballero Mena, University of Las Palmas de Gran Canaria

    Professor. Department of Mathematic

  • Kishin, University of Las Palmas de Gran Canaria

    Full Professor. Department of Mathematics,

  • Rayco, University of Las Palmas de Gran Canaria

    Professor, Department of Mathematic

References

[1] Khojasteh, F., Shukla, S., Radenovic, S.: A New Approach to the

Study of Fixed Point Theory for Simulation Functions, Filomat 29

(2015) 1189-1194.

[2] Karapinar, E.: Fixed Points Results via Simulation Functions, Filomat

30:8 (2016) 2343-2350.

[3] Guo, D., Lakshmikantham, V.: Coupled fixed points of nonlinear

operators with applications, Nonlinear Anal. Th. Methods Appl. 11

(1987) 623-632.

[4] Chen, Y.Z.: Existence theorems of coupled fixed points, J. Math. Anal.

Appl. 154 (1991) 142-150.

[5] Gnana Bhaskar, T., Lakshmikantham, V.: Fixed point theorems in

partially ordered metric spaces and applications, Nonlinear Analysis

65 (2006) 1379-1393.

[6] Samet, B.: Coupled fixed pint theorems for a generalized Meir-Keeler

contraction in partially ordered metric spaces, Nonlinear Anal. 72

(2010) 4508-4517.

[7] Luong, N.V., Thuan, N.X.: Coupled fixed points in partially ordered

metric spaces and applications, Nonlinear Analysis 74 (2011) 983-992.

[8] Urs, C.: Coupled fixed points theorems and applications to periodic

boundary value problems, Miskolc Math. Notes vol. 14 (2013) 323-333.

[9] Harjani, J., Rocha, J., Sadarangani, K.: α−Coupled fixed points

and their application in dynamic programming, Abstract and Applied

Analysis, vol. 2014, Article ID 593645, 4 pag.

[10] Afshari, H., Kalantari, S., Karapinar, E.: Solution of fractional

differential equations via coupled fixed point, Elec. J. Diff. Eq., vol.

2015 (2015) Nº 286 (1-12).

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Published

2025-03-29

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