Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSubclass of k-uniformly starlike functions defined by symmetric q-derivative operator
96
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The theory of $q$-analogs frequently occurs in a number of areas, including the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play a prominent role in the study of $q$-deformed quantum mechanical simple harmonic oscillator. In this paper, we define a symmetric $q$-derivative operator and study new family of univalent functions defined by use of that operator. We establish some new relations between functions satisfying analytic conditions related to conical sections.
rate research
Read More
In this paper, two new subclasses of bi-univalent functions related to conic domains are defined by making use of symmetric $q$-differential operator. The initial bounds for Fekete-Szego inequality for the functions $f$ in these classes are estimated.
In this paper we introduce and study two new subclasses Sigma_{lambdamu mp}(alpha,beta)$ and $Sigma^{+}_{lambdamu mp}(alpha,beta)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.
Harmonic functions are natural generalizations of conformal mappings. In recent years, a lot of work have been done by some researchers who focus on harmonic starlike functions. In this paper, we aim to introduce two classes of harmonic univalent functions of the unit disk, called hereditarily $lambda$-spirallike functions and hereditarily strongly starlike functions, which are the generalizations of $lambda$-spirallike functions and strongly starlike functions, respectively. We note that a relation can be obtained between this two classes. We also investigate analytic characterization of hereditarily spirallike functions and uniform boundedness of hereditarily strongly starlike functions. Some coefficient conditions are given for hereditary strong starlikeness and hereditary spirallikeness. As a simple application, we consider a special form of harmonic functions.
In the present paper the new multiplier transformations $mathrm{{mathcal{J}% }}_{p}^{delta }(lambda ,mu ,l)$ $(delta ,lgeq 0,;lambda geq mu geq 0;;pin mathrm{% }%mathbb{N} )}$ 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.
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii of close-to-convexity, starlikeness and convexity by using fractional calculus techniques.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
