- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 2 Issue: 1
- Some problems in the fixed point theory
Some problems in the fixed point theory
Authors : İoan A. RUS
Pages : 1-10
Doi:10.31197/atnaa.379280
View : 4 | Download : 1
Publication Date : 2018-03-25
Article Type : Research
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 stabili