PPF dependent fixed points in A-closed Razumikhin classes

TL;DR

This paper shows that PPF dependent fixed points in algebraically closed Razumikhin classes are equivalent to fixed points in constant classes and can be derived from SVV type contractions without regularity conditions.

Contribution

It simplifies existing fixed point results in Razumikhin classes by reducing them to SVV type contractions, removing the need for regularity assumptions.

Findings

PPF dependent fixed points are equivalent to fixed points in constant classes.

Fixed point results can be derived from SVV type contractions.

Regularity conditions are unnecessary for these fixed point results.

Abstract

The PPF dependent fixed point result in algebraically closed Razumikhin classes due to Agarwal et al [Fixed Point Theory Appl., 2013, 2013:280] is identical with its constant class counterpart; and this, in turn, is reducible to a fixed point principle involving SVV type contractions (over the subsequent metric space of initial Banach structure), without any regularity conditions about the Razumikhin classes. The conclusion remains valid for all PPF dependent fixed point results founded on such global conditions.