Tbilisi Mathematical Journal

An application of Perov type results in gauge spaces

Lakshmi Narayan Mishra, Animesh Gupta, and Vandana

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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.


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

Article information

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

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

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Digital Object Identifier

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]

Integral equation gauge space fixed point


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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