On Fabry's gap theorem
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 generalized Fatou theorems for the square root of the Poisson kernel and in rank one symmetric space
On growth of polynomials.
On -symmetrical functions
n the present paper the authors study some families of functions from a complex linear space into a complex linear space . They introduce the notion of -symmetrical function (; ) which is a generalization of the notions of even, odd and -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset of can be uniquely represented as the sum of an even function and an odd function.
On maximum modulus for the derivative of a polynomial
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 Phragmén-Lindelöf principle of type .
On the behavior of algebraic polynomials in regions with piecewise smooth boundary without cusps
We continue studying the estimation of Bernstein-Walsh type for algebraic polynomials in regions with piecewise smooth boundary.
On the approximation of by Re for analytic functions.
On the radius of convexity for a class of conformal maps
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
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.
On Trjitzinsky monogenic functions
On Two Functional Equations Connected with a Mean-Value Property of Polynomials
On Two Functional Equations Connected with a Mean-Value Property of Polynomials (Short Communication)
Plane elliptic systems and monogenic functions in symmetric domains
Poznámka k větě Cauchyho
Projection of analytic sets and Bernstein inequalities
Remarks on some recent results about polynomials with restricted zeros
We point out certain flaws in two papers published in Ann. Univ. Mariae Curie-Skłodowska Sect. A, one in 2009 and the other in 2011. We discuss in detail the validity of the results in the two papers in question
S. N. Bernstein type estimations in the mean on the curves in a complex plane.
Sequences, wedges and associated sets of complex numbers
Some Characterizations of L-regular Points.