In the present investigation, we use principle of subordination to introduce a new family for holomorphic functions defined by generalized differential operator. Also establish some interesting geometric properties belonging this family.

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...

the purpose of this paper is to derive various useful subordination properties and characteristics for certain subclass of multivalent meromorphic functions, which are defined here by the multiplier transformation. also, we obtained inclusion relationship for this subclass.

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this we define family of analytic non-Bazilevi? functions, denoted as Tq,?+1,u?(?,?,M,N). Furthermore, investigate differential subordination properties univalent functions using q-calculus, includes best dominance, subordination, and sandwich-type properties. Our results are proven...

In this article, we use the concept of symmetric q-calculus and convolution in order to define a q-differential operator for multivalent functions. This is an extension classical Ruscheweyh differential operator. By using technique subordination, derive several interesting applications newly defined