Existence of fixed points for \(\Theta\)-type contraction and \(\theta\)-type Suzuki contraction in complete metric spaces

DOI10.1186/s13663-016-0496-5zbMath1338.54190OpenAlexW2233494308WikidataQ59468423 ScholiaQ59468423MaRDI QIDQ269963

Yun Xiao, Xin-dong Liu, Liang Cai Zhao, Shi Sheng Zhang

Publication date: 6 April 2016

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13663-016-0496-5

zbMATH Keywords

fixed pointBanach contraction principle\(\Theta\)-type contraction\(\Theta\)-type Suzuki contraction

Mathematics Subject Classification ID

Complete metric spaces (54E50) Other nonlinear integral equations (45G10) Fixed-point and coincidence theorems (topological aspects) (54H25) Special maps on metric spaces (54E40)

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Cites Work

• Convergence theorems for some multi-valued generalized nonexpansive mappings
• Iterated function systems consisting of \(F\)-contractions
• A new type of fixed point theorem in metric spaces
• A general maximality principle and a fixed point theorem in uniform space
• Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms
• A new generalization of the Banach contraction principle
• Further generalizations of the Banach contraction principle
• Several fixed point theorems concerning \(\tau\)-distance
• On Fixed and Periodic Points Under Contractive Mappings
• Generalized distance and existence theorems in complete metric spaces