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Mishra, Lakshmi Narayan; Gupta, Animesh; Vandana

An application of Perov type results in gauge spaces. (English) Zbl 1431.54031

Tbil. Math. J. 11, No. 2, 139-151 (2018).
Summary: 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.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
47J05 Equations involving nonlinear operators (general)
45G15 Systems of nonlinear integral equations

Keywords:

integral equation; gauge space; fixed point
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\textit{L. N. Mishra} et al., Tbil. Math. J. 11, No. 2, 139--151 (2018; Zbl 1431.54031)
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