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Displaying similar documents to “Argument estimates of certain multivalent functions involving Dziok-Srivastava operator.”

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...

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...