A Study on Certain Subclasses of Analytic Functions Involving the Jackson q-Difference Operator

Lashin, A. Y.; Badghaish, Abeer O.; Algethami, Badriah Maeed

doi:10.3390/sym14071471

Cited by 5 publications

(4 citation statements)

References 38 publications

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“…Jackson in the early twentieth century. Numerous mathematical fields, including number theory, combinatorics, orthogonal polynomials, fundamental hyper-geometric functions, and other sciences, including physics and the theory of relativity, have used it successfully [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Some q-Symmetric Integral Inequalities Involving s-Convex Functions

Nosheen,

Ijaz,

Khan

et al. 2023

Symmetry

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The q-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.

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Section: Introductionmentioning

confidence: 99%

Some q-Symmetric Integral Inequalities Involving s-Convex Functions

Nosheen,

Ijaz,

Khan

et al. 2023

Symmetry

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“…In the area of geometric function theory of complex analysis, the q-derivative operator D q was used in the year 1990 by Ismail et al [29] to study a class of q-starlike functions and by Srivastava in his book chapter [30], which was published in 1989, to investigate the univalence, starlikeness and convexity properties of the generalized qhypergeometric function r Φ s involving r numerator parameters and s denominator parameters r, s ∈ N 0 := N ∪ {0} . Some recent studies, in which the q-derivative operator D q was applied to various subclasses of of the function classes A(p) (p 1), can be found in, for example, [31][32][33][34].…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Subclasses of p-Valent κ-Uniformly Convex and Starlike Functions Defined by the q-Derivative Operator

2023

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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 are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator Sη,p,qn,m. Secondly, by means of this q-derivative operator, we define an interesting subclass Tℵλ,pn,m(η,α,κ) of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk U. This p-valent analytic function class is associated with the class κ-UCV of κ-uniformly convex functions and the class κ-UST of κ-uniformly starlike functions in U. For functions belonging to the normalized analytic and multivalent (or p-valent) function class Tℵλ,pn,m(η,α,κ), we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein.

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“…Based on the same idea, many authors have extensively studied the q-calculus operators (q-differential and q-integral operators) in GFT. A recent study on these operators acting on analytic functions can be found in [12][13][14][15][16][17][18][19]. For 0 < q < 1, Jackson [9,10] defined the q-differential operator, D q , of a function, ξ, as the following:…”

Section: Introductionmentioning

confidence: 99%

Properties for a Certain Subclass of Analytic Functions Associated with the Salagean q-Differential Operator

Lashin,

Badghaish,

Alshehri

2023

Fractal Fract

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Using the Salagean q-differential operator, we investigate a novel subclass of analytic functions in the open unit disc, and we use the Hadamard product to provide some inclusion relations. Furthermore, the coefficient conditions, convolution properties, and applications of the q-fractional calculus operators are investigated for this class of functions. In addition, we extend the Miller and Mocanu inequality to the q-theory of analytic functions.

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A Study on Certain Subclasses of Analytic Functions Involving the Jackson q-Difference Operator

Cited by 5 publications

References 38 publications

Some q-Symmetric Integral Inequalities Involving s-Convex Functions

Some q-Symmetric Integral Inequalities Involving s-Convex Functions

Subclasses of p-Valent κ-Uniformly Convex and Starlike Functions Defined by the q-Derivative Operator

Properties for a Certain Subclass of Analytic Functions Associated with the Salagean q-Differential Operator

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