Fixed point theorems for operators with a contractive iterate in b-metric spaces

Monica Felicia Bota


We consider, in this paper, mappings with a contractive iterate at apoint, which are not contractions, and prove some uniqueness andexistence results in the case of b-metric spaces. A data dependence result and an Ulam-Hyers stability result are also proved.


Fixed point, $b$-metric space, contractive iterate, data dependence, Ulam-Hyers stability

Full Text:



S. Czerwik, {it Contraction mappings in $b$-metric spaces}, Acta

Mathematica et Informatica Universitatis Ostraviensis 1(1993), 5-11.

bibitem{Guseman}L. F. Guseman, Jr., emph{Fixed Point Theorems for Mappings with a Contractive Iterate at a Point}, Proceedings of the American Mathematical Society, Vol. 26, No. 4 (Dec., 1970), pp. 615-618.


I. A. Rus, emph{The theory of a metrical fixed point theorem:

theoretical and applicative relevances}, Fixed Point Theory,

(2008), No. 2, 541-559.


I. A. Rus, A. Petruc sel, A. S^{i}ntu amu arian, {it Data

dependence of the fixed points set of some multivalued weakly Picard

operators}, Nonlinear Anal. 52(2003), 1947-1959.


  • There are currently no refbacks.