Fixed point theorems for operators with a contractive iterate in b-metric spaces
Keywords:
Fixed point, $b$-metric space, contractive iterate, data dependence, Ulam-Hyers stabilityAbstract
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.References
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.
bibitem{Rus}
I. A. Rus, emph{The theory of a metrical fixed point theorem:
theoretical and applicative relevances}, Fixed Point Theory,
(2008), No. 2, 541-559.
bibitem{RPS}
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.
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