A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point

DOI10.1090/S0002-9939-08-09390-8zbMath1152.54033MaRDI QIDQ3532537

Tomonari Suzuki

Publication date: 28 October 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

fixed pointsuccessive approximationsBanach-Caccioppoli contraction principleleader mapping

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (7)

Two new types of fixed point theorems in complete metric spaces ⋮ Unnamed Item ⋮ Convergence of the sequence of successive approximations to a fixed point ⋮ A new type of fixed point theorem in metric spaces ⋮ Subrahmanyam's fixed point theorem ⋮ A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point. II ⋮ Unnamed Item

Cites Work

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• On Fixed and Periodic Points Under Contractive Mappings
• Equivalent Cauchy sequences and contractive fixed points in metric spaces
• A Generalization of Banach's Contraction Principle
• Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
• Some Results on Fixed Points--II
• Generalized distance and existence theorems in complete metric spaces

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