Geometric Properties of the Miller-Ross Functions

Eker, Sevtap Sümer; Ece, Sadettin

doi:10.1007/s40995-022-01268-8

Cited by 11 publications

(9 citation statements)

References 10 publications

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“…Proof. The inequalities ( 9) and ( 10) were proved by Eker and Ece [19]. On the other hand, by using the triangle inequality and the following inequality (see [19])…”

Section: A Set Of Lemmasmentioning

confidence: 97%

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Geometric Properties of Generalized Integral Operators Related to The Miller–Ross Function

Kazımoğlu

Deni̇z

Cotîrlǎ

2023

Axioms

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It is very well-known that the special functions and integral operators play a vital role in the research of applied and mathematical sciences. In this paper, our aim is to present sufficient conditions for the families of integral operators containing the normalized forms of the Miller–Ross functions such that they can be univalent in the open unit disk. Moreover, we find the convexity order of these operators. In proof of results, we use some differential inequalities related with Miller–Ross functions and well-known lemmas. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples.

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“…Proof. The inequalities ( 9) and ( 10) were proved by Eker and Ece [19]. On the other hand, by using the triangle inequality and the following inequality (see [19])…”

Section: A Set Of Lemmasmentioning

confidence: 97%

“…Recently, Eker and Ece [19] and Şeker et al [20] studied geometric and characteristic properties of this function, respectively. Also, some problems as partial sums, coefficient inequalities, inclusion relations and neighborhoods for Miller-Ross function were studied by Kazımo glu [21,22].…”

Section: Introductionmentioning

confidence: 99%

Geometric Properties of Generalized Integral Operators Related to The Miller–Ross Function

Kazımoğlu

Deni̇z

Cotîrlǎ

2023

Axioms

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“…The above definitions have been investigated in different studies, see for example [32][33][34][35]. Moreover, Noshiro-Warschawski [36,37] provided the following inclusion result: 𝒞 ⊂ 𝒮 * ⊂ 𝒦 ⊂ 𝒮 .…”

Section: ∑ 𝜎 𝛼 (𝑛)𝑥mentioning

confidence: 99%

Geometric Properties of a Linear Operator Involving Lambert Series and Rabotnov Function

Salah

2023

Preprint

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In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

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“…Bansal et al [15] examined some geometric properties of τ -confluent hypergeometric functions. Recently, Eker and Ece investigated geometric properties of Rabotnov functions [18] and Miller-Ross functions [17]. Motivated by these works, we obtained sufficient conditions for close-to-convexity, univalency, starlikeness and convexity of the generalized Wright-Bessel functions.…”

Section: Introductionmentioning

confidence: 99%