Some problems in the fixed point theory

Some problems in the fixed point theory

n this paper we present some of my favorite problems, all the time open, in the fixed point theory. These problems are in connection with the following two: Which properties have the fixed point equations for which an iterative algorithm is convergent ? Let us have a fixed point theorem, T, and a...

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Bibliographic Details
Main Author: Ioan A. Rus
Format: Article
Language:English
Published: ATNAA 2018-12-01
Series:Advances in the Theory of Nonlinear Analysis and its Applications
Subjects:
ordered set
L-space
metric space
Banach space
Picard operator
weakly Picard operator
fixed point
fixed point structure
iterative algorithm
retraction-displacement condition
well-posedness of fixed point problem
Ostrowski property
global asymptotic stability
open problem
conjecture
Online Access:http://dergipark.gov.tr/download/article-file/596098
Description
Summary:n this paper we present some of my favorite problems, all the time open, in the fixed point theory. These problems are in connection with the following two: Which properties have the fixed point equations for which an iterative algorithm is convergent ? Let us have a fixed point theorem, T, and an operator f (single or multivalued) which does not satisfy the conditions in T. In which conditions the operator f has an invariant subset Y such that the restriction of f to Y , f|Y , satisfies the conditions of T ?
ISSN:2587-2648
2587-2648

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