New types of multifunctions in ideal topological spaces via $e$-$\I$-Open sets and $\delta\beta$-$\I$-Open sets

Abstract

The purpose of the present paper is to introduce and investigate two new classes of continuous multifunctions called upper/lower $e$-$\I$-continuous multifunctions and upper/lower $\delta\beta_I$-continuous multifunctions by using the concepts of $e$-$\I$-open sets and $\delta\beta_I$-open sets. The class of upper/lower $e$-$\I$-continuous multifunctions is contained in that of upper/lower $\delta\beta_I$-continuous multifunctions. Several characterizations and fundamental properties concerning upper/lower $e$-$\I$-continuity and upper/lower $\delta\beta_I$-continuity are obtained.

Keywords

• e$-$\I$-open set
• $\delta\beta_I$-open set
• upper (lower) $e$-$\I$-continuous multifunctions
• upper (lower) $\delta\beta_I$-continuous multifunctions