Insertion of a Contra-α-continuous Function

Abstract

A necessary and sufficient condition in terms of lower cut sets is given for the insertion of a contra-α-continuous function between two comparable real-valued functions.

Strong Insertion of a Contra-continuous Function between Two Comparable Contra-precontinuous (Contra-semi-continuous) of Real-valued Functions

“…Several insertion theorems are obtained as corollaries of these results. In addition, the insertion and strong insertion of a contra-α-continuous function and insertion of a contra-continuous function between two comparable realvalued functions has also recently considered by the authors in [22,23,24].…”

Insertion of a Contra-continuous Function between Two Comparable Real-valued Functions

“…Several insertion theorems are obtained as corollaries of these results. In addition, the insertion and strong insertion of a contra-α-continuous function between two comparable real-valued functions has also recently considered by the authors in [20,21].…”