Some problems in the fixed point theory

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:2 Issue:1
Some problems in the fixed point theory

Some problems in the fixed point theory

Pages : 1-10

View : 11 | Download : 8

Publication Date : 2018-03-25

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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

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