Abstract
We introduce a family Q α(a, c), a ≥ 0 of functions \(f:f\left( z \right) = + \sum\nolimits_{n = 2}^\infty {{a_n}} {z^n}\) analytic in the unit disc E by using a well-known convolution operator L(a, c)f = ϕ(a, c)✶f where ϕ(a,c) is an incomplete beta function. We investigate Q α(a, c) and give some of its properties including integral representation, coefficient result, a covering theorem, and several inclusion results.
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© 1999 Springer Science+Business Media Dordrecht
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Noor, K.I. (1999). On Alpha-Quasi-Convex Functions Defined by Convolution with Incomplete Beta Functions. In: Rassias, T.M., Srivastava, H.M. (eds) Analytic and Geometric Inequalities and Applications. Mathematics and Its Applications, vol 478. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4577-0_16
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DOI: https://doi.org/10.1007/978-94-011-4577-0_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5938-1
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