Application of the product net technique and Kadec-Klee property to study nonlinear ergodic theorems and weak convergence theorems in uniformly convex multi-Banach spaces

DOI10.1186/s13660-019-1996-8zbMath1499.37004OpenAlexW2924864263MaRDI QIDQ2067757

Reza Saadati, Chun-Gil Park, Hassan Morghi Kenari

Publication date: 19 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-019-1996-8

zbMATH Keywords

asymptotically nonexpansive mappingKadec-Klee propertyalmost orbituniformly convex multi-Banach spacereversible semi-groups

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Ergodic theorems, spectral theory, Markov operators (37A30)

Cites Work

• Weak convergence and non-linear ergodic theorems for reversible semigroups of non-Lipschitzian mappings
• Amenable semigroups
• Ergodic retractions for amenable semigroups in Banach spaces with normal structure
• Existence of ergodic retractions for semigroups in Banach spaces
• Asymptotic aspect of the quadratic functional equation in multi-normed spaces
• Strong convergence of Browder's type iterations for left amenable semigroups of Lipschitzian mappings in Banach spaces
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Nonstandard methods in fixed point theory
• Existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in Banach spaces
• Nonlinear ergodic theorems for general curves defined on general semigroups.
• Weak convergence theorems for asymptotically nonexpansive mappings and semigroups
• Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups
• The mean ergodic theorem for nonexpansive mappings in multi-Banach spaces
• Convergence of ergodic means of orbits of semigroups of nonexpansive mappings in sets with the \(\varGamma\)-Opial property
• Nonlinear ergodic theorems of nonexpansive type mappings
• Mean ergodic theorem for semigroups of linear operators in multi-Banach spaces
• Nonlinear ergodic theorems and weak convergence theorems for reversible semigroup of asymptotically nonexpansive mappings in Banach spaces
• Multi-normed spaces
• Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings
• Asymptotically nonexpansive semigroups in Banach spaces
• Some problems and results in the study of nonlinear analysis
• On the asymptotic behaviour of almost-orbits of nonlinear contraction semigroups in Banach spaces
• On Asymptotically Nonexpansive Semigroups of Mappings
• Asymptotically Non-Expansive Actions of Topological Semigroups and Fixed Points
• STABILITY OF MAPPINGS ON MULTI-NORMED SPACES

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