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On Fabry's gap theorem

Jan-Christoph Puchta (2002)

Archivum Mathematicum

By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.

On ( j , k ) -symmetrical functions

Piotr Liczberski, Jerzy Połubiński (1995)

Mathematica Bohemica

n the present paper the authors study some families of functions from a complex linear space X into a complex linear space Y . They introduce the notion of ( j , k ) -symmetrical function ( k = 2 , 3 , ⋯ ; j = 0 , 1 , ⋯ , k - 1 ) which is a generalization of the notions of even, odd and k -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset U of X can be uniquely represented as the sum of an even function and an odd function.

On maximum modulus for the derivative of a polynomial

K. Dewan, Sunil Hans (2009)

Annales UMCS, Mathematica

If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

On the radius of convexity for a class of conformal maps

V. Karunakaran, K. Bhuvaneswari (2007)

Colloquium Mathematicae

Let 𝓐 denote the class of all analytic functions f in the open unit disc 𝔻 in the complex plane satisfying f(0) = 0, f'(0) = 1. Let U(λ) (0 < λ ≤ 1) denote the class of functions f ∈ 𝓐 for which |(z/f(z))²f'(z) -1| < λ for z ∈ 𝔻. The behaviour of functions in this class has been extensively studied in the literature. In this paper, we shall prove that no member of U₀(λ) = {f ∈ U(λ): f''(0) = 0} is convex in 𝔻 for any λ and obtain a lower bound for the...

On the zeros of polynomials and analytic functions

Roshan Lal, Susheel Kumar, Sunil Hans (2011)

Annales UMCS, Mathematica

For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.

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