A Class of Multivalent Functions With Negative Taylor Coefficients

Mishra, Ambuj Kumar; Choudhury, Mousumi

doi:10.1515/dema-1995-0126

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2018

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“…The classical subfamily C(α) (S * (α)), of univalent convex of order α (univalent starlike of order α, 0 ≤ α < 1), respectively were introduced and studied in [24] are found in [8,10,11]. Mishra and Choudhury [21] showed that the class S δ [α] also contains non-univalent function for negative δ. In [23], Mishra and Gochhayat found the coefficient estimate problems for inverse of functions in the class S δ [α].…”

Section: Introductionmentioning

confidence: 99%

A subclass of harmonic univalent mappings with a restricted analytic part

Chinahara,

Gochhayat,

Maharana

2018

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In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class S δ [α], 0 ≤ α < 1, −∞ < δ < ∞ which has been introduced and studied by Kumar [17] (see also [20], [21], [22], [23]). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bounds for the Bloch's constant for all functions in that family.

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Section: Introductionmentioning

confidence: 99%