On nonexpansive mappings [PDF]
Proceedings of the American Mathematical Society, 1976 A generalized Hilbert space property is used to analyze nonexpansive mappings in certain settings. In particular it is shown that in l 1
L A. Karlovitz
openaire +4 more sources
Convergence Theorems for a Maximal Monotone Operator and a 𝑉-Strongly Nonexpansive Mapping in a Banach Space [PDF]
Abstract and Applied Analysis, 2010 Let E be a smooth Banach space with a norm ‖⋅‖. Let 𝑉(𝑥,𝑦)=‖𝑥‖2+‖𝑦‖2−2⟨𝑥,𝐽𝑦⟩ for any 𝑥,𝑦∈𝐸, where ⟨⋅,⋅⟩ stands for the duality pair and J is the normalized duality mapping.
Hiroko Manaka
doaj +2 more sources
On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings [PDF]
Fixed Point Theory and Applications, 2010 We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixed-point set of a single strongly relatively nonexpansive mapping.
Saejung Satit, Nilsrakoo Weerayuth
doaj +5 more sources
On the Weak Relatively Nonexpansive Multivalued Mappings in Banach Spaces [PDF]
Abstract and Applied Analysis, 2012 In recent years, the definition of relatively nonexpansive multivalued mapping and the definition of weak relatively nonexpansive multivalued mapping have been presented and studied by many authors.
Yongfu Su
doaj +2 more sources
Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping [PDF]
Journal of Applied Mathematics, 2014 We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone
Xian Wang, Jun-min Chen, Hui Tong
doaj +2 more sources
A Remark on Nonexpansive Mappings [PDF]
Canadian Mathematical Bulletin, 1981 Let X be a closed convex subset of a Banach space and let T: X → X be a nonexpansive mapping, i.e.
Goebel, Kazimierz, Koter, Malgorzata
openaire +3 more sources
Approximating fixed points of nonexpansive and generalized nonexpansive mappings [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 في هذه الورقة، نعتبر رسم الخرائطSمن النموذجS=α0I+α1T+α2T2+...+αKTK، حيثαi≥0.α1>0مع α i=0kαi=1، ونوضح أنه في مساحة بنك محدبة بشكل موحد، تتقارب تكرارات Picard لـ S إلى نقطة ثابتة منTعندما يكونTغير موسع أو معمم غير موسع أو حتى شبه موسع.
Manoranjan Maiti, Biswajyoti Saha
openaire +5 more sources
On a Class of Generalized Nonexpansive Mappings [PDF]
Mathematics, 2020 In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.
Simeon Reich, Alexander J. Zaslavski
doaj +2 more sources
Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi-I-Nonexpansive Mapping in Banach Space [PDF]
Fixed Point Theory and Applications, 2010 We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a ...
Farrukh Mukhamedov, Mansoor Saburov
doaj +2 more sources
Convergence of Generalized Quasi-Nonexpansive Mappings in Hyperbolic Space [PDF]
Journal of Function Spaces, 2022 In this article, we consider a wider class of nonexpansive mappings (locally related quasi-nonexpansive) than monotone nonexpansive mappings. We obtained the convergence of fixed point for quasi ϱ-preserving locally related quasi-nonexpansive mappings in
Naeem Saleem +3 more
doaj +2 more sources