Perov type results in gauge spaces and applications to integral systems on semi-axis


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


Adela Novac
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


tegral equation; gauge space; fixed point

Paper coordinates

A. Novac, R. Precup, Perov type results in gauge spaces and applications to integral systems on semi-axis, Math. Slovaca 64 (2014), 961-972,


About this paper


Journal Mathematica Slovaca

Publisher Name

De Gruyter Open Ltd.

Print ISSN


Online ISSN


google scholar link

[1] Angelov, V. G.:Fixed Points in Uniform Spaces and Applications, Cluj UniversityPress, Cluj-Napoca, 2009.
[2] Chis, A.—Precup, R.:Continuation theory for general contractions in gauge spaces,Fixed Point Theory Appl.2004(2004),173–185.
[3] Colojoara, I.:Sur un theoreme de point fixe dans les espaces uniformes complets,Com.Acad.R.P.Rom.11(1961), 281–283.
[4] Cooke, K. L.—Kaplan, J. L.:A periodicity threshold theorem for epidemics andpopulation growth, Math. Biosci.31(1976), 87–104.
[5] Dugundju, J.:Topology, Allyn and Bacon, Massachusetts, 1966.
[6] Frigon, M.:Fixed point and continuation results for contractions in metric and gaugespaces. In: Fixed Point Theory and Its Applications. Banach Center Publ. 77, PolishAcad. Sci., Warsaw, 2007, pp. 89–114.
[7] Gheorghiu, N.:Contraction theorem in uniform spaces, Stud. Cerc. Mat.19(1967),119–122 (Romanian).
[8] Gheorghiu, N.:Fixed point theorems in uniform spaces, An.Stiint. Univ. Al. I. Cuza Iasi. Sect ̧. I Mat.28(1982), 17–18.
[9] Knill, R. J.:Fixed points of uniform contractions, J. Math. Anal. Appl.12(1965),449–455.
[10] Marinescu, G.:Topological and Pseudo topological Vector Spaces,EdituraAcad.R.P.Rom., Bucharest, 1959 (Romanian).
[11] Perov, A. I.—Kibenko, A. V.:On a certain general method for investigation ofboundary value problems, Izv. Akad. Nauk SSSR30(1966), 249–264 (Russian).
[12] Precup, R.:Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.
[13] Precup, R.:The role of matrices that are convergent to zero in the study of semilinearoperator systems, Math. Comput. Modelling49(2009), 703–708.
[14] Precup, R.:Existence, localization and multiplicity results for positive radial solutionsof semilinear elliptic systems, J. Math. Anal. Appl.352(2009), 48–56.
[15] Precup, R.—VIOREL, A.:Existence results for systems of nonlinear evolution inclusions, Fixed Point Theory11(2010), 337–346.
[16] Tarafdar, E.:An approach to fixed-point theorems on uniform spaces,Trans.Amer.Math. Soc.191(1974), 209–225.

Related Posts