A Novel Subclass of Univalent Functions Involving Operators of Fractional Calculus

Kamble, P. N.; Shrigan, M. G.; Srivástava, H. M.

doi:10.12732/ijam.v30i6.4

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…Various definitions of operators of fractional calculus are available in the literature (cf., e.g. [10,22,24]). Let us mention the Saigo hypergeometric operators.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

New Subclass of Bi-Univalent Functions Based on Quasi-Subordination

Ho Choi

2023

Int. J. of Appl. Math.

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In this paper, we introduce a new subclass M λ,µ,ν Σ,q (γ, δ, ϕ) of analytic and bi-univalent functions involving a certain fractional integral operator which is defined based on quasi-subordination. For this class, we estimate the second and third coefficients of the Taylor-Maclaurin series expansions and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

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“…Various definitions of operators of fractional calculus are available in the literature (cf., e.g. [10,22,24]). Let us mention the Saigo hypergeometric operators.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

New Subclass of Bi-Univalent Functions Based on Quasi-Subordination

Ho Choi

2023

Int. J. of Appl. Math.

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“…In 2014, Kanas and Rȃducanu [8] defined q-analogue of Ruscheweyh differential operator using the ideas of convolution and then studied some of its properties. Another source of information is [9]. In the same way many mathematicians explored this field and wrote some valuable articles which played important role in developing the field of Geometric function theory, for instance see the references [10][11][12][13][14].…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Some Geometric Properties of a Family of Analytic Functions Involving a Generalized q-Operator

Shi

Khan

Ahmad³

2020

Symmetry

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In analysis, the introduction of q-calculus has been a revelation. It has a deep impact on various concepts and applications of pure and applied sciences. In this article we investigate certain geometric properties relating to convolution of functions of a newly defined class of analytic functions. The important region of the lemniscate of Bernoulli is considered. Here we utilize concepts of q-calculus which enhances and generalizes the vitality of this research work. In the same context we study the Fekete–Szegö problem.

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“…In terms of the Hadamard product (or convolution), the Dziok-Srivastava linear convolution operator involving the generalized hypergeometric function was introduced and studied systematically by Dziok and Srivastava [14,15] and (subsequently) by many other authors (see, for details, [17,18,29]). We recall here a general Hurwitz-Lerch Zeta function Φ(z, s, a) defined in [31] by…”

Section: Introductionmentioning

confidence: 99%