This paper is related to notions adapted from fuzzy set theory the field of complex analysis, namely differential subordinations. work aims present new subordinations for which best dominant and subordinate are given, respectively. The original theorems proved in generate interesting corollaries particular choices functions acting as dominant. Here, this article, subordination results obtained ...

ALINA ALB LUPAS¸Abstract. In the present paper we establish several differential superordinations regarding the new operator RD m λ,α defined by using the generalized S˘ al˘ agean operator D m λ f (z) and Ruscheweyh derivative R m f ∞ j=n+1 a j z j , z ∈ U }. A number of interesting consequences of some of these superordination results are discussed. Relevant connections of some of the new resu...

By using the method of differential subordination, we obtain some sufficient conditions for strongly p-valent starlikeness.

‎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)...

Using the results of third-order differential subordination, we introduce certain families admissible functions and discuss some applications subordination for meromorphic associated with a linear operator containing generalized Mittag-Leffler function.

The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all a...

In this present investigation, we obtain some results for certain second order linear differential subordination. We also discuss some applications of our results.

‎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)...