Certain Classes of Analytic Functions Associated With q-Analogue of p-Valent Cătaş Operator

Aouf, M. K.; Madian, S. M.

doi:10.2478/mjpaa-2021-0029

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2022

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Cited by 2 publications

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“…In recent years, the topic of q-calculus had attracted the attention of several researchers (see, for example, [2,15,16,23,34,[43][44][45]). Quantum calculus is the modern name for the investigation of calculus without limits.…”

Section: Introductionmentioning

confidence: 99%

Properties of neighborhood for certain classes associated with complex order and m-q-p-valent functions with higher order

Madian

2022

J Egypt Math Soc

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In this paper, by using q-calculus (Jackson’s q-derivative) $$D_{q,p}$$ D q , p we defined new operator $$D_{\lambda ,q,p}^{n}f^{(m)}(z)$$ D λ , q , p n f ( m ) ( z ) . After that, we used this operator to introduce two new subclasses of multivalent analytic functions with complex order. Also, we obtained coefficients estimates and consequent inclusion relationships involving the $$N_{j,\delta ,m}^{p,q}(f)$$ N j , δ , m p , q ( f ) -neighborhood of these classes

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Section: Introductionmentioning

confidence: 99%

Properties of neighborhood for certain classes associated with complex order and m-q-p-valent functions with higher order

Madian

2022

J Egypt Math Soc

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Some properties for certain class of bi-univalent functions defined by $ q $-Cătaş operator with bounded boundary rotation

Madian¹

2021

MATH

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<abstract>Throughout the paper, we introduce a new subclass $ \mathcal{H}_{\alpha, \mu, \rho, m, \beta }^{n, q, \lambda, l}\ f(z)$ by using the Bazilevič functions with the idea of bounded boundary rotation and $ q $-analogue Cătaş operator. Also we find the estimate of the coefficients for functions in this class. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward $ (p, q) $-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter $ p $ is obviously redundant.</abstract>

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Certain Classes of Analytic Functions Associated With q-Analogue of p-Valent Cătaş Operator

Abstract: In this paper, we investigate several interesting properties for certain class of analytic functions defined by q-analogue of p-valent Cătaş operator. All our results are sharp.

Cited by 2 publications

References 38 publications

Properties of neighborhood for certain classes associated with complex order and m-q-p-valent functions with higher order

Properties of neighborhood for certain classes associated with complex order and m-q-p-valent functions with higher order

Some properties for certain class of bi-univalent functions defined by $ q $-Cătaş operator with bounded boundary rotation

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