In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{\beta,\alpha}$, $0

Let $\mathcal{\mathcal{S}}_{\cos}^{\ast}$ denote the class of normalized analytic functions $f$ in the open unit disk $\mathbb{D}$ satisfying the subordination $\dfrac{zf^{\prime}(z)}{f(z)}\prec\cos z$. In the second section of this article we find the sharp upper bounds for the initial coefficients $a_{3}$, $a_{4}$ and $a_{5}$ and the sharp upper bound for module of the Hankel determinant $|H_{2,3}(f)|$ for the functions from the class $\mathcal{S}_{\cos}^{\ast}$. The first result of the next section deals with the sharp upper bounds of the logarithmic coefficients $\gamma_{3}$ and $\gamma_{4}$ and we found in addition the sharp upper bound for $\left|H_{2,2}\left(F_{f}/2\right)\right|$. For obtaining these results we used the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061--2072], and the technique for finding the maximum value of a three variable function on a closed cuboid. All the maximum found values were checked by using MAPLE\texttrademark{} computare software, and we also found the extremal functions in each cases. All of our present results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596--618, 2023].

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi univalent function defined in open unit disk connected with a linear q-convolution operator, which are associated with the quasi-subordination. We find coefficients estimate |h_2 |,|h_3 | for functions in these subclasses. Several known and new consequences of these results are also pointed out.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In this study, we introduce a new class of bi-univalent functions using q-Janowski Function. We derive the Fekete-Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes are3 presented by customizing the parameters employed in our initial discoveries.

In the present paper we introduce three new classes of bi-univalent functions connected with Gregory coefficients. For functions in each of these three bi-univalent function classes we have derived the estimates of the Taylor--Maclaurin coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ and Fekete-Szeg\H{o} functional problems for functions belonging to these new subclasses. We defined three subclasses of the class of the bi-univalent functions $\Sigma$, namely $\mathfrak{HG}_{\Sigma}$, $\mathfrak{GM}_{\Sigma}(\mu)$ and $\mathfrak{G}_{\Sigma}(\lambda)$ by using the subordinations with the function whose coefficients are Gregory's numbers. First, we proved that these classes are not empty, i.e. contains other functions than the identity one. Using the well-known Carath\'eodory Lemma for the functions with real positive parts in the open unit disk, together with an estimation due to P. Zaprawa (see https://doi.org/10.1155/2014/357480) and another one of Libera and Zlotkiewicz, we gave upper bounds for the above mentioned initial coefficients and for the Fekete-Szeg\H{o} functionals. The main results are followed by some particular cases, and the novelty of the definitions and the proofs could involve further studies for such type of similarly defined subclasses.

In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fekete-Szeg\H{o} functional estimate for these classes is studied.