Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions

Certain new classes of q-convex and q-close to convex functions that involve the q-Janowski type functions have been defined by using the concepts of quantum (or q-) calculus as well as q-conic domain Ω k , q [ λ , α ] . This study explores some important geometric properties such as coefficient estimates, sufficiency criteria and convolution properties of these classes. A distinction of new findings with those obtained in earlier investigations is also provided, where appropriate.

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“…Janowski [35] initiated the class P (λ, α) by showing that p ∈ P (λ, α) if and only if there exists a mapping p ∈ P such that…”

Section: Definition 1 ([35]mentioning

confidence: 99%

“…Here, κ = cosh (πR (y)/(4R(y))) ∈ (0, 1), where R(y) is Legendre's complete elliptic integral of first kind and R (y) = R( 1 − y 2 ) is its complementary integral, see [22,23,[29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

et al. 2020

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“…In geometric function theory, the study of generalized Bessel functions is an important topic. In this study, we refer to the studies by Baricz [3][4][5][6], Akgul [1,2], Sakar and Aydogan [18], Cho et al [8] , Mondal and Swaminathan [15], Deniz [11], Deniz et al [10], and Choi and Agarwal [9]. Studies on Struve functions can be found in a recent investigation by Srivastava et al [20].…”

Section: Definition 11mentioning

confidence: 99%

Subclasses of uniformly convex and starlike functions associated with Bessel functions

Naeem¹,

Hussain²,

Sakar³

et al. 2019

Turk J Math

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In recent years, applications of Bessel differential equations have been commonly used in univalent functions theory. The main object of the present paper is to give some characteristic properties for some subclasses of uniformly starlike and convex functions which are defined here by means of the normalized form of the generalized Bessel function to be univalent in the open unit disc. Furthermore, we also establish some results of these subclasses related to a particular integral operator. Some corresponding consequences of our main results are also considered.

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“…. One could also find coefficient bounds and different properties of S * 1 (α) and C 1 (α) in [3,6,11,14,17]. Let T be the class consisting of functions of the form as:…”

Section: Introductionmentioning

confidence: 99%

An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions

Yildiz¹,

Akyar²

2020

Turk J Math

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In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters a, b , and c in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order α = 2 −r and order α = 2 −r type β = 2 −1 , with r is a positive integer.

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Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions

Cited by 5 publications

References 5 publications

Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

Subclasses of uniformly convex and starlike functions associated with Bessel functions

An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions

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