Family of mappings with an equicontractive-type condition

Autor:	Dariusz Wardowski
Rok vydání:	2020
Předmět:	Combinatorics Operator (computer programming) Applied Mathematics Modeling and Simulation Bounded function Banach space Initial value problem Hausdorff measure Geometry and Topology Fixed point Type (model theory) Complete metric space Mathematics
Zdroj:	Journal of Fixed Point Theory and Applications. 22
ISSN:	1661-7746 1661-7738
DOI:	10.1007/s11784-020-00789-2
Popis:	In a real Banach space X and a complete metric space M, we consider a compact mapping C defined on a closed and bounded subset A of X with values in M and the operator $$T:A\times C(A) \rightarrow X$$ T : A × C ( A ) → X . Using a new type of equicontractive condition for a certain family of mappings and $$\beta $$ β -condensing operators defined by the Hausdorff measure of noncompactness we prove that the operator $$x\mapsto T(x,C(x))$$ x ↦ T ( x , C ( x ) ) has a fixed point. The obtained results are applied to the initial value problem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::35b86f3fda0ace3b11a6aa223d3af2af https://doi.org/10.1007/s11784-020-00789-2 Zobrazit plný text záznamu Full text from SpringerLink