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

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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### References:

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