The main purpose of this investigation is to use quantum calculus approach and obtain the Bohr radius for the class of q-starlike (q-convex) functions of order α . The Bohr radius is also determined for a generalized class of q-Janowski st...
As an application of the well-known Sălăgean differential operator, a new operator is introduced and, using this, a new class of functions Sn(α) is defined, which has the classes of starlike and convex functions of order α as sp...
We consider the order of the strongly-starlikeness of the generalized α -convex functions. Some sufficient conditions for functions to be p-valently strongly-starlike are given.
Let the class of functions of f(z) of the form f(z)=z+∑k=2∞akzk, which are denoted by A and called analytic functions in the open-unit disk. There are many interesting properties of the functions f(z) in the class A concerning the subordina...
Let A¯ be the new general class of functions f(z) of the form f(z)=z+∑k=1∞a1+k2z1+k2 that are analytic in the open unit disc U. In the present paper, for f(z)∈A¯, we consider classes S∗¯(α), C¯(&al...
In this paper, we introduce and study the class of analytic functions in the unit disc, which are derived from Robertson’s analytic formula for starlike functions with respect to a boundary point combined with a subordination involving lemnisca...
Using several applications of the theory of differential subordination we obtain sufficient conditions for usually normalized analytic functions to belong to certain subclasses of close-to-convex functions and close-to-convex functions of order &a...
Let Σ be the class of meromorphic functions f of the form f ( ζ ) = ζ + ∑ n = 0 ∞ a n ζ − n which are analytic in Δ : = { ζ ∈ C : | ζ | > 1 } . For n...
In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order α, strong starlikeness, and some inclusion results. We also study r...
In this paper, two new classes of q-starlike functions in an open unit disc are defined and studied by using the q-fractional derivative. The class Sq*˜(α), α∈(−3,1], q∈(0,1) generalizes the class Sq* of q-starlike f...
By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this p...
The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such...
The main purpose of current paper is to obtain some new criteria for meromorphic strongly starlike functions of order α and strongly close-to-convexity of order α . Furthermore, the main results presented here are compared with...
We use a new approach to differential subordination to obtain some subordination implications for subclasses of the class of strongly starlike functions of order α.
We introduce and systematically study a new class kλ,p(α,β) of meromorphic p-valent functions defined by means of the Ruscheweyh-type operator D*λ,p, where p∈N, λ>−p, 0≤α<1, and β>0. M...
Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbol...
In this study, we consider different types of convex-exponent products of elements of a certain class of log-harmonic mapping and then find sufficient conditions for them to be starlike log-harmonic functions. For instance, we show that, if f is a sp...
The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals ar...
This paper introduces a new class related to close-to-convex functions denoted by K s k , N . This class is based on combining the concepts of starlike functions with respect to N-ply symmetry points of the order α , introduced by...
For a function p analytic in the open unit disc and satisfying p(0)=1, we prove certain subordination implications of the first order differential subordination 1+zp′(z)≺1+Mz, which provides sufficient conditions for a function to belong...
In this article, we first consider the fractional q-differential operator and the λ,q-fractional differintegral operator Dqλ:A→A. Using the λ,q-fractional differintegral operator, we define two new subclasses of analytic fun...
The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying t...
This study introduces a new integral operator Ip,μδ that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses: Σp+δ,μ,α, consisting o...
In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, ve...