Displaying similar documents to “Some subclasses of close-to-convex functions”

Uniformly convex functions II

Wancang Ma, David Minda (1993)

Annales Polonici Mathematici

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses f - 1 ( w ) = w + d ₂ w ² + d ₃ w ³ + . . . . The series expansion for f - 1 ( w ) converges when | w | < ϱ f , where 0 < ϱ f depends on f. The sharp bounds on | a n | and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on | a n | and all extremal functions for...

Large dimensional sets not containing a given angle

Viktor Harangi (2011)

Open Mathematics

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We say that a set in a Euclidean space does not contain an angle α if the angle determined by any three points of the set is not equal to α. The goal of this paper is to construct compact sets of large Hausdorff dimension that do not contain a given angle α ∈ (0,π). We will construct such sets in ℝn of Hausdorff dimension c(α)n with a positive c(α) depending only on α provided that α is different from π/3, π/2 and 2π/3. This improves on an earlier construction (due to several authors)...

Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points

Nihat Yagmur, Halit Orhan (2014)

Mathematica Bohemica

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The authors obtain the Fekete-Szegő inequality (according to parameters s and t in the region s 2 + s t + t 2 < 3 , s ≠ t and s + t ≠ 2 , or in the region s 2 + s t + t 2 > 3 , s ≠ t and s + t ≠ 2 ) for certain normalized analytic functions f ( z ) belonging to k -UST λ , μ n ( s , t , γ ) which satisfy the condition ℜ ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) > k ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) - 1 + γ , z ∈ 𝒰 . Also certain applications of the main result a class of functions defined by the Hadamard product (or convolution) are given. As a special case of this result, the Fekete-Szegő inequality for a class of functions defined through fractional derivatives...