SOME PROPERTIES OF q CLOSE-TO-CONVEX FUNCTIONS

Uçar, Hatice Esra Özkan; Mert, Oya; Polatoğlu, Yaşar

doi:10.15672/hjms.2017.459

Cited by 7 publications

(4 citation statements)

References 3 publications

(3 reference statements)

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“…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

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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.

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“…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

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“…This was the amazing breakthrough by which two different fields, q-calculus and the theory of analytic functions, were linked. After this interesting investigation, certain subclasses of analytic functions were defined and examined in terms of q-function theory by several scholars; we refer to [21][22][23][24][25][26][27][28][29][30]. The study of q-operators plays a vital role in the development of this field of study.…”

Section: Introductionmentioning

confidence: 99%

On Generalizations of the Close-to-Convex Functions Associated with q-Srivastava–Attiya Operator

et al. 2023

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The study of the q-analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the q-difference operator. Moreover, by using the q-analogues of a certain family of linear operators, the classes Kq,bsh, K˜q,sbh, Qq,bsh, and Q˜q,sbh are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the q-Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration.

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“…Some properties related with q-function theory were first introduced by Ismail et al [11]. Moreover, several authors studied many applications of q-calculus associated with generalized subclasses of analytic functions; see [2,19,21,28]. The study of linear operators plays an important and vital role in the field of geometric function theory.…”

Section: Introductionmentioning

confidence: 99%