The concept of $\delta\text{-}{\beta}_{\mathcal{I}}$-paracompactness in ideal topological spaces is introduced as a weaker form of $\beta$-paracompactness, which was looked at in \cite{YO}. This study examines several characterizations of $\delta\text{-}{\beta}_{\mathcal{I}}$-paracompact spaces and its subsets. Furthermore, we investigate the invariants of $\delta\text{-}{\beta}_{\mathcal{I}}$-paracompactness through functions.

This paper presents new concepts of continuous multifunctions defined from an ideal topological space into a bitopological space, called upper weakly $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions and lower weakly $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions. Furthermore, several characterizations and some properties concerning upper weakly $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions and lower weakly $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions are investigated. Moreover, the relationships between almost $\tau^\star(\sigma_1,\sigma_2)$-continuity andweak $\tau^\star(\sigma_1,\sigma_2)$-continuity are established.

This paper presents new concepts of continuous multifunctions defined between an ideal topological space and a bitopological space, namely upper almost $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions. Moreover, several characterizations and some properties concerning upper almost $\tau^\star(\sigma_1,\sigma_2)$-continuousmultifunctions and lower almost $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions are considered. Furthermore, the relationships between $\tau^\star(\sigma_1,\sigma_2)$-continuity and almost $\tau^\star(\sigma_1,\sigma_2)$-continuity are discussed.

This paper presents new concepts of continuous multifunctions defined from an ideal topological space into a bitopological space, called upper $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions and lower $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions. Furthermore, several characterizations and some properties concerning upper $\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions and lower$\tau^\star(\sigma_1,\sigma_2)$-continuous multifunctions are investigated.

This paper presents new classes of multifunctions called upper nearly $(\tau_1,\tau_2)$-continuousmultifunctions and lower nearly $(\tau_1,\tau_2)$-continuous multifunctions. Furthermore, some characterizations of upper nearly $(\tau_1,\tau_2)$-continuous multifunctions and lower nearly $(\tau_1,\tau_2)$-continuous multifunctions are established.