Property preserving operators
1989 ◽
Vol 39
(3)
◽
pp. 397-404
Keyword(s):
Let S denote the class of functions of the form that are analytic and univalent in |z| < 1. Given f ∈ S and a, b, c, real numbers other than 0, −1, −2,…, let Ω(a, b, C; f) = F(a, b, C; z)* f(z) where is a hypergeometric Gauss function with (a)0 = 1 and (a)k = a(a + 1) … (a + k − 1) and * denotes the Hadamard product. For qn(z) = z + a2z2 + … + anzn (an ≠ 0, n = 5,6) in S, it is shown that , is univalent in |z| < 1. This extends the result previously known for n = 3 and n = 4. Also, we obtain a necessary and sufficient condition involving a, b, and c such that Ω(a, b, c;·) preserves the subclass of S consisting of starlike functions of order α, 0 ≤ α ≤ 1, with ak 0.
1984 ◽
Vol 95
(1)
◽
pp. 21-23
1975 ◽
Vol 12
(01)
◽
pp. 130-134
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New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function
2018 ◽
Vol 85
(3-4)
◽
pp. 411
1912 ◽
Vol 87
(594)
◽
pp. 225-229
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