Some problems in the fixed point theory
Copyright policy )Some problems in the fixed point theory
In this paper we present some of my favorite problems, all the time open, in the fixed point theory. Theseproblems 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 satisfythe conditions in T. In which conditions the operator f has an invariant subset Y such that the restrictionof f to Y , fY , satisfies the conditions of T ?
- Babeș-Bolyai University Romania
Matematik, 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, Mathematical Sciences
Matematik, 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, Mathematical Sciences
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