Tbilisi Mathematical Journal

An application of Perov type results in gauge spaces

Lakshmi Narayan Mishra, Animesh Gupta, and Vandana

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Abstract

In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghiu’s sense on spaces endowed with a family of vector valued pseudo-metrics. Applications to systems of integral equations are given to illustrate the theory. The examples also prove the advantage of using vector valued pseudo-metrics and matrices that are convergent to zero, for the study of systems of equations.

Note

The author would like to thank the editor and the referees for their valuable suggestions for improving the article.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 2 (2018), 139-151.

Dates
Received: 2 February 2017
Accepted: 30 March 2018
First available in Project Euclid: 6 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1530842676

Digital Object Identifier
doi:10.32513/tbilisi/1530842676

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 45G15: Systems of nonlinear integral equations
Secondary: 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25]

Keywords
Integral equation gauge space fixed point

Citation

Mishra, Lakshmi Narayan; Gupta, Animesh; Vandana. An application of Perov type results in gauge spaces. Tbilisi Math. J. 11 (2018), no. 2, 139--151. doi:10.32513/tbilisi/1530842676. https://projecteuclid.org/euclid.tbilisi/1530842676


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