2014
DOI: 10.1155/2014/260198
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Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function

Abstract: By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.

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Cited by 2 publications
(5 citation statements)
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“…. This implies that the desired in equality (6) holds. If f (z) = z (|z| = r < 1), then there exist a coefficient 1+c k+c δ a k = 0 for some k ≥ 2.…”
Section: Conditions For Functions To Be In the Classmentioning
confidence: 79%
See 3 more Smart Citations
“…. This implies that the desired in equality (6) holds. If f (z) = z (|z| = r < 1), then there exist a coefficient 1+c k+c δ a k = 0 for some k ≥ 2.…”
Section: Conditions For Functions To Be In the Classmentioning
confidence: 79%
“…Proof. In view of Theorem 1 we need only to prove that f ∈ TΦ δ c (λ, β) satisfies the coefficient inequality (6)…”
Section: Conditions For Functions To Be In the Classmentioning
confidence: 99%
See 2 more Smart Citations
“…New strong differential sandwich-type results associated with the generalized derivative operator are also obtained. Using various linear operators, strong differential subordinations were investigated by Jeyaraman et al [8], Cho [5], and AL-Shaqsi [3] and of course many others.…”
Section: Introductionmentioning
confidence: 99%