Rates of convergence for iterative solutions of equations involving set-valued accretive operators

U Kohlenbach, T Powell - Computers & Mathematics with Applications, 2020 - Elsevier
This paper studies proofs of strong convergence of various iterative algorithms for computing
the unique zeros of set-valued accretive operators that also satisfy some weak form of …

[PDF][PDF] Proof Mining for Nonlinear Operator Theory: Four Case Studies on Accretive Operators, the Cauchy Problem and Nonexpansive Semigroups

A Koutsoukou-Argyraki - 2017 - tuprints.ulb.tu-darmstadt.de
We present the first applications of proof mining to the theory of partial differential equations
as well as to set-valued operators in Banach spaces, in particular to abstract Cauchy …

Effective rates of convergence for the resolvents of accretive operators

A Koutsoukou-Argyraki - Numerical Functional Analysis and …, 2017 - Taylor & Francis
We extract explicit, computable, and highly uniform rates for the strong convergence of the
resolvents of set-valued, m-accretive, and uniformly accretive at zero/ϕ-expansive operators …

Constructing zeros of accretive operators

S Reich - Applicable Analysis, 1979 - Taylor & Francis
Constructing zeros of accretive operators<xref ref-type='fn' rid='FN0001'></xref> Page 1
Applzcubie Annljsis. 1979. Vol. 8, pp. 349-352 0 Gordon and Breach Sclence Pubhshers Ltd …

Logical metatheorems for accretive and (generalized) monotone set-valued operators

N Pischke - Journal of Mathematical Logic, 2024 - World Scientific
Accretive and monotone operator theory are central branches of nonlinear functional
analysis and constitute the abstract study of certain set-valued mappings between function …

Effective metastability for a method of alternating resolvents

B Dinis, P Pinto - arXiv preprint arXiv:2101.12675, 2021 - arxiv.org
A generalized method of alternating resolvents was introduced by Boikanyo and Moro {\cs}
anu as a way to approximate common zeros of two maximal monotone operators. In this …

[PDF][PDF] On zeros of accretive operators with application to the convex feasibility problem

A Nandal, R Chugh - UPB Sci. Bull. Ser. A, 2019 - scientificbulletin.upb.ro
In this paper, we study some iterative algorithms for finding common zeros of finite family of
accretive operators in Banach spaces. Our results improve the recent results of Kim and …

On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators

H Cui, M Su - Applied Mathematics and Computation, 2015 - Elsevier
Given two real sequences (rn) and (α n), we study the iterative scheme: x n+ 1= α n u+(1-α n)
J rnxn, for finding a zero of an accretive operator A, where u is a fixed element and J rn …

Constructing zeros of accretive operators II

S Reich, P Gilbert, AB Bakušinskii, BT Poljak… - Applicable …, 1979 - Taylor & Francis
In a preceding paper we proved a convergence theorem for an implicit iterative scheme, and
then applied it to an explicit one. In the present paper we study a modification of this …

A proof-theoretic metatheorem for nonlinear semigroups generated by an accretive operator and applications

N Pischke - arXiv preprint arXiv:2304.01723, 2023 - arxiv.org
We further develop the theoretical framework of proof mining, a program in mathematical
logic that seeks to quantify and extract computational information from prima facienon …