On the order of strongly starlikeness of strongly convex functions

Nunokawa, Mamoru

doi:10.3792/pjaa.69.234

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Cited by 112 publications

(41 citation statements)

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“…The key for the improvement previous results is the following theorem and very often applied Nunokawa's lemma (Nunokawa 1993). …”

Section: Resultsmentioning

confidence: 99%

On Starlikeness of Libera Transform

Nunokawa¹,

Sokół²

2015

JSM

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“…The key for the improvement previous results is the following theorem and very often applied Nunokawa's lemma (Nunokawa 1993). …”

Section: Resultsmentioning

confidence: 99%

On Starlikeness of Libera Transform

Nunokawa¹,

Sokół²

2015

JSM

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“…denotes the class of strongly convex functions of order β. Analogously to (1.1), in the work [5] it was proved that if β ∈ (0, 1) and f ∈ SK(α(β)), then f ∈ SS(β), where…”

Section: Introductionmentioning

confidence: 86%

Strongly gamma-starlike functions of order alpha

Nunokawa

Sokół

2013

Annales UMCS, Mathematica

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Abstract. In this work we consider the class of analytic functions G(α, γ), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Złotkiewicz in Gamma starlike functions, Ann. Univ. Mariae CurieSkłodowska, Sect. A 28 (1974), 53-58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass. Introduction.Let H denote the class of analytic functions in the unit disc D = {z : |z| < 1} on the complex plane C. For a ∈ C and n ∈ N we denote byso A = A 1 . Let S be the subclass of A whose members are univalent in D.The class S * α of starlike functions of order α < 1 may be defined as2000 Mathematics Subject Classification. Primary 30C45, Secondary 30C80. Key words and phrases. Strongly starlike functions of order alpha, convex functions of order alpha, strongly starlike functions of order alpha, gamma-starlike functions, Nunokawa's Lemma.

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“…To prove the main results, we also need the following generalization of the Nunokawa's lemma, [4], [5].…”

Section: Introductionmentioning

confidence: 99%