Third-order differential subordination results for analytic functions involving the generalized Bessel functions

Tang, Huo; Deni̇z, Erhan

doi:10.1016/s0252-9602(14)60116-8

Cited by 34 publications

(23 citation statements)

References 19 publications

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“…Let Q be the set of analytic and univalent functions q on the set U \ E(q), where E(q) = {ξ : ξ ∈ ∂U and lim z→ξ q(z) = ∞}, and are such that min |q (ξ)| = ρ > 0 for ξ ∈ ∂U \ E(q). Further, let the subclass of Q for which q(0) = a be written by Q(a) and 6,32,34]). Let ψ : C 4 × U → C and h(z) be univalent in U.…”

Section: Definition 11 ([6]mentioning

confidence: 99%

“…More recently, Antonino and Miller [6] introduced the notion of third-order differential subordination, and Tang and Deniz [32] studied the third-order differential subordination results for analytic functions involving the generalized Bessel functions. Later on, Tang et al [33] introduced the notion of third-order differential superordination and also studied the corresponding third-order differential superordination involving the generalized Bessel functions.…”

Section: Definition 15 ([33])mentioning

confidence: 99%

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Third-order differential sandwich-type results involving the Liu-Owa integral operator

Tang¹,

Aouf²,

Owa³

et al. 2018

J. Math. Computer Sci.

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Section: Definition 11 ([6]mentioning

confidence: 99%

Section: Definition 15 ([33])mentioning

confidence: 99%

Third-order differential sandwich-type results involving the Liu-Owa integral operator

Tang¹,

Aouf²,

Owa³

et al. 2018

J. Math. Computer Sci.

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“…Baricz et al [10] (see also [33]) introduced a new operator B c κ : A → A, which is defined by means of the Hadamard product (or convolution) as follows:…”

Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

“…Recently, Tang and Deniz [33] have considered the applications of these results to third-order differential subordination for analytic functions in U.…”

Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

Third-Order Differential Superordination Involving the Generalized Bessel Functions

Tang

Srivástava

Deni̇z

et al. 2014

Bull. Malays. Math. Sci. Soc.

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There are many articles in the literature dealing with the first-order and the second-order differential subordination and differential superordination problems for analytic functions in the unit disk, but there are only a few articles dealing with the third-order differential subordination problems. The concept of third-order differential subordination in the unit disk was introduced by Antonino and Miller, and studied recently by Tang and Deniz. Let be a set in the complex plane C, let p(z) be analytic in the unit disk U = {z : z ∈ C and |z| < 1}, and let ψ : C 4 ×U → C. In this paper, we investigate the problem of determining properties of functions p(z) that satisfy the following third-order differential superordination:As applications, we derive some third-order differential superordination results for analytic functions in U, which are associated with a family of generalized Bessel functions. The results are obtained by considering suitable classes of admissible functions. New third-order differential sandwich-type results are also obtained.

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“…In 2014, Tang et al [35] investigated some thirdorder differential subordination results for analytic functions involving the generalized Bessel functions. In 2014, Tang et al [36] studied the differential superordination based on analytic functions involving the generalized Bessel functions.…”

mentioning

confidence: 99%

Third-order differential subordination and superordination involving a fractional operator

2015

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Abstract:The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

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Third-order differential subordination results for analytic functions involving the generalized Bessel functions

Cited by 34 publications

References 19 publications

Third-order differential sandwich-type results involving the Liu-Owa integral operator

Third-order differential sandwich-type results involving the Liu-Owa integral operator

Third-Order Differential Superordination Involving the Generalized Bessel Functions

Third-order differential subordination and superordination involving a fractional operator

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