On a Certain Subclass of p-Valent Analytic Functions Involving q-Difference Operator

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

doi:10.3390/sym15010093

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…If the derivative and integral concepts in these models are replaced with q-and q, ω-analogs, new problems and new fields of study are created and solution methods are sought. Some recent works related to q-calculus include in [19,25,26,35,36,39] (also cited therein), and studies on q-calculus up to 2000 can be seen in [15]. Although the q, ω-derivative was defined in the 1950s, the q, ω-calculus subject is a newer field of study since the q, ω-inverse derivative (integral) was defined in 2009.…”

Section: Introductionmentioning

confidence: 99%

On q,ω -differential transform method

Hıra¹

2023

J. Phys. A: Math. Theor.

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In this study, the differential transform method (DTM) associated with the Hahn difference operator ( D q , ω ) has been examined. The definitions and theorems of the one and two-dimensional q , ω -DTM are introduced. Then, the presented q , ω -DTMs are applied to obtain the analytical or approximation solution of linear or non-linear q , ω -initial value problems consisting of the q , ω -ordinary or q , ω -partial differential equation.

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Section: Introductionmentioning

confidence: 99%

On q,ω -differential transform method

Hıra¹

2023

J. Phys. A: Math. Theor.

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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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Certain results on a class of analytic functions involving q-hypergeometric series

Bhardwaj

Sharma

2023

Asian-European J. Math.

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Based on [Formula: see text]-Hypergeometric Series, a linear operator [Formula: see text] is considered and involving this operator a class [Formula: see text] of analytic functions is defined by using [Formula: see text]-derivatives. As a special case, a class [Formula: see text] by involving [Formula: see text]-analogue of Hohlov operator [Formula: see text] is defined. Coefficient inequality for a function [Formula: see text] to be in the class [Formula: see text] is obtained. Further, in terms of subordination, an equivalent condition for a function [Formula: see text] to be in this class is given and using this equivalent class condition results on coefficient estimates including Fekete–Szegö inequality and a convolution result are obtained.

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On a Certain Subclass of p-Valent Analytic Functions Involving q-Difference Operator

Cited by 3 publications

References 29 publications

On q,ω -differential transform method

On q,ω -differential transform method

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

Certain results on a class of analytic functions involving q-hypergeometric series

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