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The purpose of the present paper is to determine lower bounds for $\Re \left\}\frac{{ℰ}_{k}f\left(z\right)}{{\left({ℰ}_{k}f\right)}_m\left(z\right)}\right\{$, $\Re \left\}\frac{{\left({ℰ}_{k}f\right)}_m\left(z\right)}{{ℰ}_{k}f\left(z\right)}\right\{,\Re \left\}\frac{{ℰ}_k^{\text{'}}f\left(z\right)}{{\left({ℰ}_{k}f\right)}_m^{\text{'}}\left(z\right)}\right\{$ and $\Re \left\}\frac{{\left({ℰ}_{k}f\right)}_m^{\text{'}}\left(z\right)}{{ℰ}_k^{\text{'}}f\left(z\right)}\right\{$, where ${ℰ}_{k}f$ is the generalized normalized error function of the form ${ℰ}_{k}f\left(z\right)=z+{\sum }_{n=2}^{\infty }\frac{{\left(-1\right)}^{n-1}}{(\left(n-1\right)k+1)\left(n-1\right)!}{z}^n$ and ${\left({ℰ}_{k}f\right)}_m$ its partial sum. Furthermore, we give lower bounds for $\Re \left\}\frac{𝕀\left[{ℰ}_{k}f\right]\left(z\right)}{{\left(𝕀\left[{ℰ}_{k}f\right]\right)}_m\left(z\right)}\right\{$ and $\Re \left\}\frac{{\left(𝕀\left[{ℰ}_{k}f\right]\right)}_m\left(z\right)}{𝕀\left[{ℰ}_{k}f\right]\left(z\right)}\right\{$, where $𝕀\left[{ℰ}_{k}f\right]$ is the Alexander transform of ${ℰ}_{k}f$. Several examples of the main results are also considered.

In this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered.

We introduce and study two certain classes of holomorphic and bi-univalent functions associating $\lambda$-pseudo-starlike functions with Sakaguchi-type functions. We determine upper bounds for the Taylor–Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions belonging to these classes. Further we point out certain special cases for our results.

The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes ${\mathrm{𝒮𝒫}}_p(\alpha ,\beta )$ and ${\mathrm{𝒰𝒞𝒱}}_p(\alpha ,\beta )$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.