Certain classes of multivalent functions with negative coefficients associated with a convolution structure

Making use of a convolution structure, we introduce a new class of analytic functions $mathbb{T}^{p}_{g}(lambda,alpha, beta, )$ defined in the open unit disc and investigate its various characteristics. Further we obtained distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to the class $mathbb{T}^{p}_{g}(lambda,alpha, beta).

Some New Inclusion and Neighborhood Properties for Certain Multivalent Function Classes Associated with the Convolution Structure

We use the familiar convolution structure of analytic functions to introduce two new subclasses of multivalently analytic functions of complex order, and prove several inclusion relationships associated with the (,)-neighborhoods for these subclasses. Some interesting consequences of these results are also pointed out

A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator

Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results. © 2022, The Author(s)

Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries

Some Properties of Bazilevič Functions Involving Srivastava–Tomovski Operator

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and Fekete–Szegö functional for functions belonging to the class

Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions is defined. Making use of the operator $\mathrm{{\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l),$ two new subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out

On a Certain Subclass of Meromorphic Functions Defined by a New Linear Differential Operator

In this article, a new linear differential operator I^k (L_s^a (a_l,b_m )f(z)) is defined by using the Hadamard product of the q-hypergeometric function and a function related to the Hurwitz-Lerch zeta function. By using this linear differential operator, a new subclass L_(s,a)^(k,*) (α_l,β_m;A,B,b) of meromorphic functions is defined. Some properties and characteristics of this subclass are considered. These include the coefficient inequalities, the growth and distortion properties and the radii of meromorphic starlikeness and meromorphic convexity. Finally, closure theorems and extreme points are introduced