Subclass of starlike functions associated with a limacon

Yunus, Yuzaimi; Halim, Suzeini Abdul; Akbarally, Ajab Bai

doi:10.1063/1.5041667

Cited by 27 publications

(13 citation statements)

References 16 publications

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“…Raina and Sokol [10] used subordinations for coefficient estimation of starlike functions. Similar kinds of works have also been done by Sharma et al [11] by using starlikeness for cardioid function, and Yunus et al [12] studied for limacon.…”

Section: Introductionsupporting

confidence: 55%

Sufficiency Criteria for $q$ -Starlike Functions Associated with Cardioid

Zainab

Shakeel

Imran

et al. 2021

Journal of Function Spaces

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This article deals with the q -differential subordinations for starlike functions associated with the lemniscate of Bernoulli and cardioid domain. The primary goal of this work is to find the conditions on γ for 1 + γ z ∂ q h z / h n z ≺ 1 + z , where h z is analytic function and is subordinated by the function which is producing cardioid domain as its image domain while mapping the open unit disk. Along with this, certain sufficient conditions for q -starlikeness of analytic functions are determined.

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Section: Introductionsupporting

confidence: 55%

Sufficiency Criteria for $q$ -Starlike Functions Associated with Cardioid

Zainab

Shakeel

Imran

et al. 2021

Journal of Function Spaces

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“…For various choices of ψ and a detailed discussion about classes we refer to the papers [5][6][7][8][9].…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

Masih

Kanas

2020

Symmetry

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Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ′ ( z ) / f ( z ) or 1 + z f ″ ( z ) / f ′ ( z ) respectively are lying in the region bounded by the limaçon ( u − 1 ) 2 + v 2 − s 4 2 = 4 s 2 u − 1 + s 2 2 + v 2 , where 0 < s ≤ 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given.

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“…Using the concept of subordination, several subclasses of analytic functions were defined by condition (1.3) on the basis of geometrical interpretation of the image domain p(U). Some interesting geometrical structures are like right half plane [7], circular disk [9], conic domain [1,10,11,13], cardioid domain [14,22], generalized conic domains [16], oval and petal type domains [17], leaf-like domain [2,3,21,26], Bernoulli lemniscate [12,24] and the most concerning one is the shelllike curve [4-6, 8, 19, 20, 23, 25]. A general approach to the classes of functions defined by subordination (1.3) can be found in [15].…”

Section: Introductionmentioning

confidence: 99%

On starlike functions associated with cardioid domain

Zainab

Raza

Sokół

2021

Publ Inst Math (Belgr)

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Analytic functions are characterized by the geometry of their image domains. That?s why, geometry of image domain is of substantial importance to have a comprehensive study of analytic functions. To introduce and study new geometrical structures as image domain and to define their subsequent analytic functions is an ongoing part of research in geometric function theory. We introduced a new domain named as cardioid domain and defined the corresponding analytic function, see [14]. Here we further study the cardioid domain, to define and study starlike functions associated with cardioid domain.

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Subclass of starlike functions associated with a limacon

Cited by 27 publications

References 16 publications

Sufficiency Criteria for $q$ -Starlike Functions Associated with Cardioid

Sufficiency Criteria for $q$ -Starlike Functions Associated with Cardioid

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

On starlike functions associated with cardioid domain

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Subclass of starlike functions associated with a limacon

Cited by 27 publications

References 16 publications

Sufficiency Criteria for q -Starlike Functions Associated with Cardioid

Sufficiency Criteria for q -Starlike Functions Associated with Cardioid

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

On starlike functions associated with cardioid domain

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Sufficiency Criteria for $q$ -Starlike Functions Associated with Cardioid

Sufficiency Criteria for $q$ -Starlike Functions Associated with Cardioid