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MR3098564 Reviewed Al-Thagafi, M. A.; Shahzad, Naseer Krasnosel'skii-type fixed-point results. J. Nonlinear Convex Anal. 14 (2013), no. 3, 483–491. (Reviewer: Calogero Vetro) 47H10 (47H09)

2014
The Krasnosel'skii fixed-point theorem is a powerful tool in dealing with various types of integro-differential equations. The initial motivation of this theorem is the fact that the inversion of a perturbed differential operator may yield the sum of a continuous compact mapping and a contraction mapping.
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MR3136189 Reviewed Merghadi, F.; Godet-Thobie, C. Common fixed point theorems under contractive conditions of integral type in symmetric spaces. Demonstratio Math. 46 (2013), no. 4, 757–780. (Reviewer: Pasquale Vetro) 47H10 (47H09)

2014
The problem of establishing the existence of fixed points for mappings satisfying weak contractive conditions in metric spaces has been widely investigated in the last few decades. More recently, many papers have been published extending this study to various metric contexts.
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Nonlinear Ergodic Theorems and Weak Convergence Theorems

Journal of the Mathematical Society of Japan, 1982
Norimichi Hirano
exaly  

Nonlinear Ergodic Theorems for Nonexpansive Mappings in Hilbert Spaces

Kodai Mathematical Journal, 1979
Norimichi Hirano, Wataru Takahashi
exaly  

Iterating Holomorphic Self-Mappings of the Hilbert Ball

Proceedings of the Japan Academy Series A: Mathematical Sciences, 1982
Simeon Reich, Kazimierz Goebel
exaly  

The Existence of Nonexpansive Retractions in Banach Spaces

Journal of the Mathematical Society of Japan, 1986
Norimichi Hirano, Wataru Takahashi
exaly  

Omega Limit Sets of Nonexpansive Maps: Finiteness and Cardinality Estimates

Differential and Integral Equations, 1990
Roger D Nussbaum
exaly  

Continuous Solutions of a Nonlinear Integral Equation on an Unbounded Domain

Journal of Integral Equations and Applications, 1994
Armando Majorana
exaly  

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