$p\imath$-Сontinuity and weak $p\imath$-continuity

Abstract

In this paper, we introduce the concepts of $p\imath$-continuous multifunctions and weakly $p\imath$-continuous multifunctions by utilizing the notion of pre-$\mathscr{I}$-open sets in ideal topological spaces. We also investigate some characterizations of $p\imath$-continuous multifunctions and weakly $p\imath$-continuous multifunctions. Furthermore, the relationships between $p\imath$-continuous multifunctions and weakly $p\imath$-continuous multifunctions are discussed.