The generalized retraction methods in fixed point theory for nonself operators (Q2925803)

In this work, the author proposes an approach to some well-known fixed point results under mild contractive conditions (Caristi-Kirk theorem, Jachymski theorem, etc.)\ through the so-called generalized retraction methods.NEWLINENEWLINEA~mapping \(f: Y\to X\), where \(Y\subseteq X\) and \(X\) carries some structure with it, is called retractable with respect to the retraction \(\rho: X\to Y\) if the fixed point set of \(f\) coincides with that of the composition \(\rho\circ f\). Several results are obtained out of the classical ones by adding the condition that the nonself operator \(f\) is retractable for a certain retraction.