Some problems in the fixed point theory

Year 2018, Volume: 2 Issue: 1, 1 - 10, 25.03.2018

İoan A. Rus

https://doi.org/10.31197/atnaa.379280

Cited By: 3

Abstract

In 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 , fY , satisfies the conditions of T ?

Keywords

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

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