Coefficient inequality for q-starlike functions

Uçar, Hatice Esra Özkan

doi:10.1016/j.amc.2015.12.008

Cited by 40 publications

(12 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Specially, the theory of univalent functions can be newly described by using the theory of the q-calculus. In recent years, such q-calculus operators as the fractional q-integral and fractional q-derivative operators were used to construct several subclasses of analytic functions (see, for example [12], [18], [20], [25]). In the present paper we study the symmetric q-operator, and related problems involving univalent functions.…”

Section: Definition 12 ([7]mentioning

confidence: 99%

Subclass of k-Uniformly Starlike Functions Defined by the Symmetric q-Derivative Operator

2019

View full text Add to dashboard Cite

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.2010 Mathematics Subject Classification: 30C45, 33C45

show abstract

Section: Definition 12 ([7]mentioning

confidence: 99%

Subclass of k-Uniformly Starlike Functions Defined by the Symmetric q-Derivative Operator

2019

View full text Add to dashboard Cite

show abstract

“…In fact, the theory of univalent functions can be described by using the theory of the q-calculus. Moreover, in recent years, such q-calculus operators as the fractional q-integral and fractional q-derivative operators were used to construct several subclasses of analytic functions (see, for example, [1], [6], [26], [27], [33], [35], [36], [37] and [38]). In particular, Purohit and Raina [36] investigated applications of fractional q-calculus operators to define several classes of functions which are analytic in the open unit disk U.…”

Section: Introduction Definitions and Notationsmentioning

confidence: 99%

Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator

Srivástava

Altınkaya

Yalçın

2018

Filomat

View full text Add to dashboard Cite

In this paper, we discuss the various properties of a newly-constructed subclass of the class of normalized bi-univalent functions in the open unit disk, which is defined here by using a symmetric basic (or q-) derivative operator. Moreover, for functions belonging to this new basic (or q-) class of normalized biunivalent functions, we investigate the estimates and inequalities involving the second Hankel determinant.

show abstract

“…The class S * q of q-starlike functions was introduced in [4] and has been studied in [7,8,9,10,12,13,14,15,16,20,21,22].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Hankel Determinant Problem for q-strongly Close-to-Convex Functions

Noor

2022

EJMS

View full text Add to dashboard Cite

In this paper, we introduce a new class $K_{q}(\alpha), \quad 0<\alpha \leq1, \quad 0<q<1, $ of normalized analytic functions $f $ such that $\big|\arg\frac{D_qf(z)}{D_qg(z)}\big| \leq \alpha \frac{\pi}{2},$ where $g$ is convex univalent in $E= \{z: |z|<1\} $ and $D_qf $ is the $q$-derivative of $f $ defined as: $$D_qf(z)= \frac{f(z)-f(qz)}{(1-q)z}, \quad z\neq0\quad D_qf(0)= f^{\prime}(0). $$ The problem of growth of the Hankel determinant $H_n(k) $ for the class $K_q(\alpha) $ is investigated. Some known interesting results are pointed out as applications of the main results.

show abstract

Coefficient inequality for q-starlike functions

Cited by 40 publications

References 2 publications

Subclass of k-Uniformly Starlike Functions Defined by the Symmetric q-Derivative Operator

Subclass of k-Uniformly Starlike Functions Defined by the Symmetric q-Derivative Operator

Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator

Hankel Determinant Problem for q-strongly Close-to-Convex Functions

Contact Info

Product

Resources

About