Open AccessA common property to generalized contractions and existence of fixed points
Author(s) -
Sfya Benahmed
Publication year - 2022
Publication title -
mathematica
Language(s) - English
Resource type - Journals
eISSN - 2601-744X
pISSN - 1222-9016
DOI - 10.24193/mathcluj.2022.1.06
Subject(s) - fixed point , property (philosophy) , metric space , mathematics , fixed point property , set (abstract data type) , function (biology) , space (punctuation) , metric (unit) , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , computer science , philosophy , economics , operations management , epistemology , evolutionary biology , biology , programming language , operating system
The definitions of several types of generalized contractions for an application T from a complete metric space (X,d) in itself are recalled and reviewed. A common property [H] to all these concepts is put in light. We observe that assumption [H] is fulfilled in many cases and we prove that assumption [H] and lower semi-continuity of the function x maps to d(x,T(x)) ensure existence of a fixed point along with a sharp estimate for the distance to the fixed-points set.