Fixed Points for Operators on Generalized Metric Spaces

Adrian Petrus¸el; Ioan A. Rus; Marcel Adrian S¸erban

Authors

Adrian Petrus¸el Department of Applied Mathematics, Babe¸s-Bolyai University Cluj-Napoca, Kogalniceanu 1, 400084, Cluj-Napoca, Romania.
Ioan A. Rus Department of Applied Mathematics, Babe¸s-Bolyai University Cluj-Napoca, Kogalniceanu 1, 400084, Cluj-Napoca, Romania.
Marcel Adrian S¸erban Department of Applied Mathematics, Babe¸s-Bolyai University Cluj-Napoca, Kogalniceanu 1, 400084, Cluj-Napoca, Romania.

Keywords:

Generalized metric in the sense of Luxemburg, Pompeiu-Hausdorff generalized functional, weakly Picard operator, fixed point, strict fixed point, generalized contraction, fibre generalized contraction, data dependence, pseudo-contractive multivalued operator

Abstract

The purpose of this paper is to present the fixed point theory for operators (single valued and multivalued) on generalized metric spaces in the sense of Luxemburg.