Results 51 to 60 of about 1,168,012 (202)
Remarks about a paper dealing with the equivalence of Mann and Ishikawa iterations
Journal of Numerical Analysis and Approximation Theory, 2004 We give an affirmative answer to the following question: are Mann and Ishikawa iterations equivalent under the assumptions that \(\lim_{n\rightarrow\infty }\alpha_{n}\neq0\;\) and \(\lim_{n\rightarrow\infty}\beta_{n}\neq0\)?
Ştefan M Şoltuz
doaj +2 more sources
Are adaptive Mann iterations really adaptive?
Mathematical Communications, 2009 We show that the Adaptive Mann Iterations deserve to be named in such way. Namely, we will show that they adapt to the properties of the operator, even if the information on these properties are not known to the Mann Iteration a-priori. We will also show on an example that the Adaptive Mann Iterations perform better numerically than the usual Mann ...
Kamil S. Kazimierski +1 more
openaire +3 more sources
Inertial Krasnoselskii-Mann Iterations
Set-Valued and Variational AnalysisAbstractWe establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting.
Juan José Maulén +2 more
openaire +3 more sources
Krasnoselskii–Mann Iterations: Inertia, Perturbations and Approximation
Journal of Optimization Theory and ApplicationsAbstract This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure their weak, strong and linear convergence, either matching or improving previous results obtained ...
Daniel Cortild, Juan Peypouquet
openaire +4 more sources
Uniform asymptotic regularity for Mann iterates
Journal of Mathematical Analysis and Applications, 2002 In a previous paper we obtained an effective quantitative analysis of a theorem due to Borwein, Reich and Shafrir on the asymptotic behavior of general Krasnoselski-Mann iterations for nonexpansive self-mappings of convex sets C in arbitrary normed spaces.
openaire +2 more sources
A MANN ITERATIVE REGULARIZATION METHOD FOR ELLIPTIC CAUCHY PROBLEMS [PDF]
Numerical Functional Analysis and Optimization, 2001 We investigate the Cauchy problem for linear elliptic operators with $C^\infty$-coefficients at a regular set $Ω\subset R^2$, which is a classical example of an ill-posed problem. The Cauchy data are given at the manifold $Γ\subset \partialΩ$ and our goal is to reconstruct the trace of the $H^1(Ω)$ solution of an elliptic equation at $\partial Ω/ Γ ...
Heinz W. Engl, A. Leitão
openaire +2 more sources
Fixed Point Theory and Applications, 2007 Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L≥1, then it is shown that to each ...
K. N. V. V. Vara Prasad, G. V. R. Babu
doaj +1 more source
On the Mann iteration process in a Hilbert space
Journal of Mathematical Analysis and Applications, 1977 T. Hicks, J. Kubicek
semanticscholar +3 more sources
Implicit Mann Type Iteration Method Involving Strictly Hemicontractive Mappings in Banach Spaces [PDF]
, 2012 We proved that the modified implicit Mann iteration process can be applied to approximate the fixed point of strictly hemicontractive mappings in smooth Banach ...
Shin Min Kang, Arif Rafiq
core +1 more source
Several Fixed Point Theorems in Convex b-Metric Spaces and Applications
Mathematics, 2020 Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces.
Lili Chen +3 more
doaj +1 more source