Abstract
This paper introduces new classes of continuous multifunctions defined between an ideal topological space and a bitopological space, called upper almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions. Moreover, several characterizations and some properties concerning upper almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions are established.

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