Fixed Points for Operators on Generalized Metric Spaces

Fixed Points for Operators on Generalized Metric Spaces

CUBO A Mathematical Journal
Vol.10, N¯o 04, (45–66). December 2008
Fixed Points for Operators on Generalized Metric Spaces
Adrian Petruşel, Ioan A. Rus and Marcel Adrian Şerban
Department of Applied Mathematics,
Babeş-Bolyai University Cluj-Napoca,
Kogălniceanu 1, 400084, Cluj-Napoca, Romania
emails: petrusel{iarus, mserban}@math.ubbcluj.ro
ABSTRACT
The purpose of this paper is to present the fixed point theory for operators (singlevalued
and multivalued) on generalized metric spaces in the sense of Luxemburg.
RESUMEN
El proposito de este artı́culo es presentar la teoria de punto fijo para operadores (univariados y multivaluados) sobre espacios métricos generalizados en el sentido de Luxemburg.
Key words and phrases: 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.
Math. Subj. Class.: 47H10, 54H25.