A note on convolution of Janowski type functions with q-derivative

In this paper, we introduce new subclasses of analytic functions in the open unit disc. Furthermore, the necessary and sufficient conditions for the Poisson distribution series to be in these new subclasses are found.

In this paper, new subclasses of analytic functions in the open unit disk which are defined using generalized integral operator are introduced. Several interesting properties of these classes are obtained, such as inclusion relationships and integral preserving properties are derived.

Geometric function theory combines geometric tools and their applications for information and communication analysis. It is also successfully used in the field of advanced signals, image processing, machine learning, speech and sound recognition. Various new subclasses of analytic functions have been defined using quantum calculus to investigate many interesting properties of these subclasses. This article defines a new class of q-starlike functions in the open symmetric unit disc ∇ using symmetric quantum calculus. Extreme points for this class as well as coefficient estimates and closure theorems have been investigated. By fixing several coefficients finitely, all results were generalized into families of analytic functions.

A study of a special family of analytic functions at infinity

The main objective of this paper is to introduce and study the generality differential operator involving the q-Mittag-Leffler function on certain subclasses of analytic functions. Also, we investigate the inclusion properties of these classes, by using the concept of subordination between analytic functions.

In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator Dr. We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which Drl′(z)ϑzDrl′(z)Drl(z)1−ϑ≺ez (0≤ϑ≤1) lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained.

New subclass of analytic functions in conical domain associated with a linear operator

In the article we introduce several new subclasses of analytic functions associated with pedal shaped functions. By using differential subordination and convolution operator theory, we obtain the bound estimations of the coefficients $ a_2 $ and $ a_3 $, and the logarithmic coefficients $ d_1 $ and $ d_2 $ as well as Fekete-Szego type functional inequalities for these subclasses.

In this paper, we introduce and study some new subclasses of analytic functions defined in the open unit disc using the convolution technique. Inclusion results, radius problems and several other properties of these classes are discussed. Key words: Convolution integral operator, functions with positive real part, alpha-starlike, bounded Mocanu variation, univalent.

The estimation of the upper bound for certain coefficient relations of various subclasses of analytic functions is an active topic of research in Geometric function theory. In this paper, certain subclasses of Sakaguchi type functions are defined by subordinating to sine function in the open unit disc E = {z : |z| < 1} and some coefficient inequalities such as Fekete-Szegö inequality, Second Hankel determinant, Zalcman functional and third Hankel determinant are investigated.

The purpose of the present paper is to find a necessary and sufficient condition for Miller-Ross-type Poisson distribution series to be in the class 𝒲δ(α, γ, β) of analytic functions with negative coefficients .Also, we investigate several inclusion properties of the classes 𝒮∗, 𝒦 and ℝτ(A, B) associated of the operator 𝕀ν,c m defined by this distribution. Further, we consider an integral operator related to Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered.

The main objective of this paper is to introduce and investigate various properties and characteristics of a unified class of analytic functions with negative coefficient in the unit disc. The results presented here involve distortion inequalities and growth and distortion theorem involving fractional integrals and fractional derivatives. Keywords: Analytic functions; Univalent functions; Riemann - Liouville operators ; Growth and distortion theorem; Fractional derivatives.

<abstract><p>In recent years, many authors have studied and investigated majorization results for different subclasses of analytic functions. In this paper, we give some majorization results for certain non vanishing analytic functions, whose ratios are subordinated to different domains in the open unit disk.</p></abstract>

This paper attempts to determine the “largest” sets of local univalence for a given class and the “largest” open sets in which all functions belonging to a given class are univalent. We establish general properties of sets of univalence for analytic functions with typical normalization. Moreover, we determine some examples of the sets of univalence for some particular subclasses of analytic functions.

In this paper, we introduce and study a new subclass of analytic functions which are defined by means of a linear operator. Some results connected to coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity close-to-convexity and integral means inequalities related to the subclass is obtained.