Javascript must be enabled to continue!

A note on the convergence of Mann iteration

The main result in this note slightly generalizes Theorem 3.4 in [S¸ t. Maruster and I. A. Rus, ˘ Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 3, 171–180]. We also significantly improve its proof. Both results in the paper are based on the concepts of demicontractivity and quasi-expansivity and involve relatively weak conditions that guarantee the convergence of Krasnoselskij method (the same conditions are not sufficient for the convergence of Picard iteration). Thus, our note is a satisfactory answer to the following question: if for a given mapping some specific conditions for the convergence of Picard iteration are not satisfied (and presumptively the Picard iteration fails to converge), what are the conditions which still ensure the convergence of the Mann iteration?

Technical University of Cluj Napoca, North University Center of Baia Mare

Ștefan Mărușter

Creative Mathematics and Informatics

2021

Title: A note on the convergence of Mann iteration

Description:

The main result in this note slightly generalizes Theorem 3.

4 in [S¸ t.

Maruster and I.

Rus, ˘ Kannan contractions and strongly demicontractive mappings, Creat.

Math.

Inform.

, 24 (2015), No.

3, 171–180].

We also significantly improve its proof.

Both results in the paper are based on the concepts of demicontractivity and quasi-expansivity and involve relatively weak conditions that guarantee the convergence of Krasnoselskij method (the same conditions are not sufficient for the convergence of Picard iteration).

Thus, our note is a satisfactory answer to the following question: if for a given mapping some specific conditions for the convergence of Picard iteration are not satisfied (and presumptively the Picard iteration fails to converge), what are the conditions which still ensure the convergence of the Mann iteration?.

Back

Related Results

Ary Scheffer, een Nederlandse Fransman

AbstractAry Scheffer (1795-1858) is so generally included in the French School (Note 2)- unsurprisingly, since his career was confined almost entirely to Paris - that the fact that...

Pieter Saenredam: zijn boekenbezit en zijn relatie met de landmeter Pieter Wils

AbstractAn earlier article on Saenredam's construction drawings (Note, 1 ) left open the question of how he obtained his knowledge of perspective. His teacher Frans de Grebber (Not...

Unbounded Star Convergence in Lattices

Let L be a vector lattice, "(" x_α ") " be a L-valued net, and x∈L . If |x_α-x|∧u→┴o 0 for every u ∈〖 L〗_+ then it is said that the net "(" x_α ")" unbounded order converges ...

Een serie tekeningen van Johannes Stradanus met scènes uit het leven van de Heilige Giovanni Gualberto

AbstractAmong the extensive collection of pen sketches by Johannes Stradanus (Bruges 1523-Florence 1605) in the Cooper-Hewitt Museum of Design and the Pierpont Morgan Library in Ne...

FA Mann’s Conservative Revolution

Abstract FA Mann led a revolution: displacing gold in the legal imagination. This chapter discusses Mann’s revolution—and today’s reaction. Mann’s tactics were brill...

Richard Wagner’s Essays and musical-dramatic output as a source of Thomas Mann’s inspiration.

The research topic of the article focuses only on the question of Wagner’s influence on Mann. Thomas Mann is considered the writer most obsessed with music. The purpose of the arti...

Semi-Convergence Analysis of Uzawa Splitting Iteration Method for Singular Saddle Point Problems

In this paper, we propose the Uzawa splitting iteration method for solving a class of singular saddle point problems. The semi-convergence of the Uzawa splitting iteration method i...

On the convergence, stability and data dependence results of the JK iteration process in Banach spaces

Abstract This article analyzes the JK iteration process with the class of mappings that are essentially endowed with a condition called condition (E). The convergenc...

Email:
Password:

Email: