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New stability results of picard iteration for contractive type mappings

Timiş J.

Fasciculi Mathematici

2016

Nr 56

167--184

There exists several concepts of stability for fixed point iterative methods in literature. The aim of this paper is to compare two such concepts, namely one due to Harder and the second one due to Rus, in the class of contractive mappings.

A fixed point result for φ-contractions on b-metric spaces without the boundedness assumption

Păcurar M.

Fasciculi Mathematici

2010

Nr 43

127-137

Starting from a result in [V. Berinde,Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory (Preprint), "Babeş-Bolyai" University of Cluj-Napoca, 3 (1993), 3-9 ], we prove the existence and uniqueness of the fixed points for φ-contractions on b-metric spaces. We also build a theory of this fixed point result.