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In this investigation, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions. Some of our results improve previous results.

In this paper we introduce and investigate three new subclasses of $p$-valent analytic functions by using the linear operator $D_{\lambda ,p}^m(f*g)\left(z\right)$. The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for $(n,\theta )$-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions $f\left(z\right)\in 𝒜$ for which $1+\frac{1}{b}\left(\frac{z{\left(D_{\alpha ,\beta ,\lambda ,\delta }^{n}f\left(z\right)\right)}^{\text{'}}}{D_{\alpha ,\beta ,\lambda ,\delta }^{n}f\left(z\right)}-1\right)$ ($\alpha ,\beta ,\lambda ,\delta \ge 0$; $\beta >\alpha$; $\lambda >\delta$; $b\in {ℂ}^{*}$; $n\in {\mathbb{N}}_0$; $z\in U$) lies in a region starlike with respect to $1$ and is symmetric with respect to the real axis.

We introduce two classes of analytic functions related to conic domains, using a new linear multiplier Dziok-Srivastava operator $D_{\lambda ,\ell }^{n.q,s}$ $(n\in {\mathbb{N}}_0=\{0,1,\cdots \}$, $q\le s+1$; $q,s\in {\mathbb{N}}_0$, $0\le \alpha <1$, $\lambda \ge 0$, $\ell \ge 0).$ Basic properties of these classes are studied, such as coefficient bounds. Various known or new special cases of our results are also pointed out. For these new function classes, we establish subordination theorems and also deduce some corollaries of these results.