Study on the q-analogue of a certain family of linear operators

Shah, Shujaat Ali; Noor, Khalida İnayat

doi:10.3906/mat-1907-41

Cited by 39 publications

(23 citation statements)

References 18 publications

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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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“…For example, the convolution theory, enable us to investigate various properties of analytic functions. Due to the large range of applications of q-calculus and the importance of q-operators instead of regular operators, many researchers have explored q-calculus in depth, such as, Kanas and Reducanu [9], Muhammad and Sokol [10] and Noor et al [11][12][13][14][15]. Also in [1-5, 9, 16-22], Ahmad et al see also [21], have used the q-derivative operator to define a new subclass q-meromorphic starlike functions.…”

Section: Introductionmentioning

confidence: 99%

Coefficient Inequalities for a Subclass of Symmetric q ‐Starlike Functions Involving Certain Conic Domains

Khan

Aracı

et al. 2022

Journal of Mathematics

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In this paper, we make use of a certain Ruscheweyh-type q -differential operator to introduce and study a new subclass of q -starlike symmetric functions, which are associated with conic domains and the well-known celebrated Janowski functions in D . We then investigate many properties for the newly defined functions class, including for example coefficients inequalities, the Fekete–Szegö Problems, and a sufficient condition. There are also relevant connections between the results provided in this study and those in a number of other published articles on this subject.

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“…Recently, in [18], Shah and Noor introduced the q-analogue of Srivastava-Attiya operator J s q,b : A → A by…”

Section: Introductionmentioning

confidence: 99%

“…It is observed that, if co-analytic part of f = h + g is identically zero, then the modified q-Srivastava-Attiya operator defined by (1.4) turn out to be the q-Srivastava-Attiya operator introduced in [18].…”

Section: Introductionmentioning

confidence: 99%