Results 21 to 30 of about 1,172,576 (205)

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
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On a Class of Generalized Nonexpansive Mappings

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 In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.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

Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces [PDF]

Fixed Point Theory and Applications, 2009
We introduce two iterative algorithms for nonexpansive mappings in Hilbert spaces. We prove that the proposed algorithms strongly converge to a fixed point of a nonexpansive mapping T.
Yonghong Yao, Yeong Cheng Liou, Giuseppe Marino   +2 more
doaj   +3 more sources

On Asymptotically Nonexpansive Semigroups of Mappings

Canadian Mathematical Bulletin, 1970
A selfmapping f of a metric space (X, d) is nonexpansive (ε-nonexpansive) if d(f(x), f(y)) ≤ d(x, y) for all x, y ∊ X (respectively if d(x, y) < ε). In [1], M.
Holmes, R. D., Narayanaswami, P. P.
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Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

Abstract and Applied Analysis, 2014
We define a mean nonexpansive mapping T on X in the sense that Tx-Ty≤ax-y+bx-Ty, a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness ...
Zhanfei Zuo
doaj   +2 more sources

On extremal nonexpansive mappings

Zeitschrift für Analysis und ihre Anwendungen
We study the extremality of nonexpansive mappings on a non-empty bounded, closed, and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banach spaces with the Radon–Nikodym property and all
Christian Bargetz, Michael Dymond, Katriin Pirk   +2 more
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Demiclosedness Principles for Generalized Nonexpansive Mappings [PDF]

Journal of Optimization Theory and Applications, 2020
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas-Rachford algorithm. We provide extensions
Sedi Bartz, Rubén Campoy, Hung M. Phan
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ORBITALLY NONEXPANSIVE MAPPINGS [PDF]

Bulletin of the Australian Mathematical Society, 2015
We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.
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Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-ϕ-Nonexpansive Mapping and Relatively Nonexpansive Mapping [PDF]

, 2010
We prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-ϕ-nonexpansive ...
Min Liu, Shih-Sen Chang, Ping Zuo
core   +1 more source

Strong Convergence Theorems for Nonexpansive Mapping [PDF]

Journal of Systems Science and Complexity, 2007
Let \(C\) be a closed convex subset of a uniformly smooth Banach space \(E\) and \(T\) a nonexpansive selfmap of \(C\) with \(F(T) \neq \emptyset\). Given a point \(u \in C\) and an initial guess \(x_0 \in C\), the author proves the strong convergence of the iteration scheme defined by \(z_n = \gamma_nx_n + (1 - \gamma_n)Tx_n\), \(y_n = \beta_nx_n + (1
Yongfu Su, Xiaolong Qin
openaire   +3 more sources