Some applications of the first-order differential subordinations

Cho, Nak Eun; Lee, Hyo‐Jeong; Park, Ji Hyang; Srivastava, Rekha

doi:10.2298/fil1606465c

Cited by 9 publications

(3 citation statements)

References 9 publications

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“…Nunokawa et al [3] proved that if 1 + zp ′ (z) ≺ 1 + z hold, the subordination p(z) ≺ 1 + z also hold. There are more results obtained by many other researchers, see [4], [5], [6], [7], [8], [9] and [10].…”

Section: Introductionmentioning

confidence: 98%

First Order Differential Equation Sudordination Associated With Cassini Curve

Hern¹,

Omar²,

Janteng³

2021

Int. J. of Appl. Math.

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Section: Introductionmentioning

confidence: 98%

First Order Differential Equation Sudordination Associated With Cassini Curve

Hern¹,

Omar²,

Janteng³

2021

Int. J. of Appl. Math.

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“…Recently, Kumar and Ravichandran [9] determined some sufficient conditions for certain first order differential subordinations to imply that the corresponding analytic solution is subordinate to a rational, exponential, or sine function. For more details, see [3,19,22,24]. The function √ 1 + z is associated with the class S * L , introduced by Sokó l and Stankiewicz [23].…”

Section: Introductionmentioning

confidence: 99%

Applications of first order differential subordination for functions with positive real part

Ahuja

Kumar

Ravichandran

2018

Stud. Univ. Babes-Bolyai Math.

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Sharp estimates on β are determined so that an analytic function p defined on the open unit disk in the complex plane normalized by p(0) = 1 is subordinate to some well known starlike functions with positive real part whenever 1 + βzp ′ (z), 1 + βzp ′ (z)/p(z), or 1 + βzp ′ (z)/p 2 (z) is subordinate to √ 1 + z. Our results provide sharp version of previously known results.2010 Mathematics Subject Classification. 30C45, 30C80.

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“…These nonsharp results provide sufficient conditions for normalized analytic functions to be in the class of the Janowski starlike functions and in the class of functions associated with the lemniscate of Bernoulli. For more details, see [3,5,6,21,27,33].…”

Section: Introductionmentioning

confidence: 99%

Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

2018

Turk J Math

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Abstract:We obtain several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with the Booth lemniscate. These results are proved by applying the well-known theory of differential subordination developed by Miller and Mocanu and these inclusions give sufficient conditions for normalized analytic functions to belong to some subclasses of Ma-Minda starlike functions. In addition, by proving an associated technical lemma, we compute various radii constants such as the radius of starlikeness, radius of convexity, radius of starlikeness associated with the lemniscate of Bernoulli, and other radius estimates for functions in the class of functions associated with the Booth lemniscate. The results obtained are sharp.

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Some applications of the first-order differential subordinations

Abstract: The object of the present paper is to give some applications of the first-order differential subordinations. We also extend and improve several previously known results.

Cited by 9 publications

References 9 publications

First Order Differential Equation Sudordination Associated With Cassini Curve

First Order Differential Equation Sudordination Associated With Cassini Curve

Applications of first order differential subordination for functions with positive real part

Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

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