In this investigation, using Opoola differential Operator ($D^{m}(\mu,\beta,t)f(z)$), a new Integral Operator: $I_{t,\beta,\mu}^{m,\sigma}(f_{1},...,f_{n})(z): A^{n}\rightarrow A$  is defined in the unit disk, $U=\left\lbrace z\in C:\left|z\right|<1\right\rbrace$; and we investigated the Univalence conditions of this generalized Operator. Finally, a number of corollaries and remarks which show the extension of our results are presented.

In this paper, we consider a general Integral Operator Gn(z). The main object of the present paper is to study some properties of this Integral Operator on the classes S* (a), K (a), M (b), N (b) and KD (m, b).

We give a brief survey of recent work on Integral forms in vertex Operator algebras (VOAs).

Let $\mathfrak{A}$ be an algebra. A \textit{derivation} on $\mathfrak{A}$ is a linear mapping $\delta:\mathfrak{A}\to\mathfrak{A}$ such that $\delta(ab)=\delta(a)b+a\delta(b)$ for every $a,b\in\mathfrak{A}$. As a dual to this notion, we consider a linear mapping $\Delta:\mathfrak{A}\to\mathfrak{A}$ with the property $\Delta(a)\Delta(b)=\Delta(\Delta(a)b+a\Delta(b))$ for every $a,b\in\mathfrak{A}$ and we call it an \textit{integration}. In this paper, we give some examples, counterexamples and facts concerning integrations on algebras. Furthermore, we state and prove a characterization for integrations on finite dimensional matrix algebras.

The proposed study is focused to introduce a novel Integral transform op-erator, called Generalized Bivariate (GB) transform. The proposed trans-form includes the features of the recently introduced Shehu transform, ARA transform, and Formable transform. It expands the repertoire of existing Laplace-type bivariate transforms. The primary focus of the present work is to elaborate fashionable properties and convolution theorems for the proposed transform Operator. The existence, inversion, and duality of the proposed transform have been established with other existing transforms. Implementation of the proposed transform has been demonstrated by ap-plying it to different types of differential and Integral equations. It validates the potential and trustworthiness of the GB transform as a mathematical tool. Furthermore, weighted norm inequalities for Integral convolutions have been constructed for the proposed transform Operator.

The object of this paper is to investigate some inclusion relationships and a number of other useful properties among certain subclasses of analytic and p-valent functions, which are defined here by certain Integral Operator.