Fixed Point Theorems for Nonexpansive Mappings and Related Classes of Mappings

1981 ◽  
pp. 182-232 ◽  
Author(s):  
Vasile I. Istrăţescu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings

scholarly journals Remarks on ”Some new fixed point theorems for contractive and nonexpansive mappings”

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6483-6491
Author(s):  
Rajendra Pant ◽  
Hemant Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Ultrametric Spaces

Pant [Filomat 28 (2014), no. 2, 313-317] obtained some fixed point results in ultrametric spaces. Unfortunately, the proofs of main results had flaws. We present corrected proofs of his theorems for single valued mappings and correct formulations and proofs in the multivalued case.

scholarly journals A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Convex Sets ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Modular Space ◽  
Ordinate Axis ◽  
Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

scholarly journals Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xianbing Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Bounded Sets

It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.

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