publication . Article . 2004

Fixed points for some non-obviously contractive operators defined in a space of continuous functions

Cezar Avramescu; Cristian Vladimirescu;
Open Access English
  • Published: 01 Feb 2004 Journal: Electronic Journal of Qualitative Theory of Differential Equations (issn: 1417-3875, eissn: 1417-3875, Copyright policy)
  • Publisher: University of Szeged
Abstract
Let $X$ be an arbitrary (real or complex) Banach space, endowed with the norm $\left| \cdot \right| .$ Consider the space of the continuous functions $C\left( \left[ 0,T\right] ,X\right) $ $\left( T>0\right) $, endowed with the usual topology, and let $M$ be a closed subset of it. One proves that each operator $A:M\rightarrow M$ fulfilling for all $x,y\in M$ and for all $t\in \left[ 0,T\right] $ the condition \begin{eqnarray*} \left| \left( Ax\right) \left( t\right) -\left( Ay\right) \left( t\right) \right| &\leq &\beta \left| x\left( \nu \left( t\right) \right) -y\left( \nu \left( t\right) \right) \right| + \\ &&+\frac{k}{t^{\alpha }}\int_{0}^{t}\left| x\left( ...
Subjects
free text keywords: Mathematics, QA1-939, Fixed point, Operator (computer programming), Banach space, Continuous function, Mathematical analysis, Discrete mathematics
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publication . Article . 2004

Fixed points for some non-obviously contractive operators defined in a space of continuous functions

Cezar Avramescu; Cristian Vladimirescu;