Upper and lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to be: {1)} upper-$(\alpha, $\alpha(F^{+}(\delta(V)))\setminus \beta(F^{+}(\theta(V)))\in \mathcal{I}$ for each open subset $V$ of $Y$;\{2)} lower-$(\alpha, if$\alpha(F^{-}(\delta(V)))\setminus \beta(F^{-}(\theta(V)))\in $Y$;\ {3)} it upper-\ %$(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuousand \beta,\theta,\delta,\mathcal{I})$-continuous. In particular, the following statements proved article (Theorem 2):Let $\theta, \theta^{*}, \delta$ \sigma)$:
 \noi\ \ {1.} The $(\alpha,\beta,\theta\cap \theta^{*},\delta,\mathcal{I})$-continuous only both $(\alpha,\beta,\theta,\delta,\mathcal{I})$-continuous $(\alpha,\beta,\theta^{*},\delta,\mathcal{I})$-continuous.
 {2.} $(\alpha,\beta,\theta^{*},\delta,\mathcal{I})$-continuous,provided that $\beta(A\cap B) =\beta(A)\cap \beta(B)$ any $A,B$