Author
Stefan Maruster
Bio: Stefan Maruster is an academic researcher from West University of Timișoara. The author has contributed to research in topics: Newton's method & Local convergence. The author has an hindex of 7, co-authored 26 publications receiving 133 citations.
Papers
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TL;DR: A new simple algorithm for solving some variational inequality in Banach spaces is constructed and it is proved that the proposed algorithm has strong convergence.
27 citations
TL;DR: A regularized variant of the Krasnoselski-Mann iteration that can be alternatively regarded as a simplified form of the inertial iteration and a new and simpler proof is proposed for its convergence even when involving non-constant relaxation factors.
21 citations
TL;DR: A new class of demicontractive mappings (called alpha-demicontractive) is introduced for which the strong convergence of the computed sequence is assured, concerning strong convergence properties of the Mann iteration.
20 citations
01 Jan 2015
13 citations
TL;DR: A formula of error estimation of Mann iteration is given in the case of strongly demicontractive mappings and a condition of strong convergence is obtained for the same class of mappings.
9 citations
Cited by
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Book•
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01 Jan 1982
TL;DR: Theorem of Borsuk and Topological Transversality as mentioned in this paper, the Lefschetz-Hopf Theory, and fixed point index are the fundamental fixed point theorem.
Abstract: Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index
688 citations
TL;DR: In this paper, the Atangana-Baleanu fractional integral of order of a function f (t ) I t ∝ s AB ζ ( t ) = 1 - ∝ B ( ∝ ) ζ( t ) + ∝ b ∝ Γ( ∝) ∫ 0 t ε ( ρ ) ( t - ρ) ∝ - 1 d ρ ; where 0 ∝ ⩽ 1, 0 t s and it is worthy to mention B ( 0 ) and B ( 1 ) are equal
Abstract: In this article, we introduce an extended F -metric and proved related fixed point results. Subsequently, we mainly focus on (a): Solution for the Atangana-Baleanu fractional integral of order ∝ of a function f ( t ) I t ∝ s AB ζ ( t ) = 1 - ∝ B ( ∝ ) ζ ( t ) + ∝ B ( ∝ ) Γ ( ∝ ) ∫ 0 t ζ ( ρ ) ( t - ρ ) ∝ - 1 d ρ ; where 0 ∝ ⩽ 1 , 0 t s and it is worthy to mention B ( 0 ) and B ( 1 ) are equal to 1. (b): L P type solution ( 1 p ∞ ) for the linear Fredholm integral equation of the second kind where
64 citations
TL;DR: Some variants of the Mann iteration that ensure the strong convergence, like the (CQ) algorithm and a variant for the asymptotically demicontractive mappings are considered.
55 citations
TL;DR: Inverse problems in image processing are typically cast as optimization tasks, consisting of data fidelity and stabilizing regularization terms as discussed by the authors, and a recent regularization strategy of great interest u...
Abstract: Inverse problems in image processing are typically cast as optimization tasks, consisting of data fidelity and stabilizing regularization terms. A recent regularization strategy of great interest u...
42 citations
Journal Article•
TL;DR: In this paper, a basic inequality in [3] is refined and improved in this paper and thus the effectiveness of an improved algorithm compared with that of the original one, is enhanced and the monotonicity of the underlying function is not required in the convergence analysis of the new algorithm.
Abstract: A basic inequality in [3] is refined and improved in this paper and thus the
effectiveness of an improved algorthm, compared with that of the original one, is enhanced
Furthermore, the monotonicity of the underlying function is not required in the convergence analysis of the new algorithm
40 citations