Results 1 to 10 of about 364 (83)

On some geometric results for generalized k-Bessel functions

Demonstratio Mathematica, 2023
The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized kk-Bessel functions, such as the radii of uniform convexity and of α\alpha -convexity.
Toklu Evrim
doaj   +1 more source

SERIES IN LE ROY TYPE FUNCTIONS: INEQUALITIES AND CONVERGENCE THEOREMS

, 2021
In studying the behaviour of series defined by means of the Le Roy type functions, we prove Cauchy–Hadamard type theorems. Asymptotic formulae for these new special functions in the cases of ‘large’ values of indices are also provided, as necessary in ...
J. Paneva-Konovska
semanticscholar   +1 more source

On the Erdős-Lax inequality concerning polynomials

Mathematical Inequalities & Applications, 2020
If P(z) is a polynomial of degree n which does not vanish in |z| < k , where k 1 , then N. K. Govil [On a theorem of S. Bernstein, Proc. Nat. Acad. Sci., 50 (1980), 50–52] proved that max |z|=1 |P′(z)| n 1+ kn max |z|=1 |P(z)|, provided |P′(z)| and |Q′(z)
G. Milovanović, A. Mir
semanticscholar   +1 more source

The growth and value distribution of Laplace-Stieltjes transformations with infinite order in the right half-plane

Journal of Inequalities and Applications, 2013
By introducing the concept of XU-order functions, we study the growth of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half-plane.
H. Xu, Z. Xuan
semanticscholar   +2 more sources

Generalization of a theorem of Clunie and Hayman [PDF]

, 2010
Clunie and Hayman proved that if the spherical derivative ‖f ′‖ of an entire function satisfies ‖f ′‖(z) = O(|z|σ) then T (r, f) = O(rσ+1). We generalize this to holomorphic curves in projective space of dimension n omitting n hyperplanes in general ...
Matthew Barrett, A. Eremenko
semanticscholar   +1 more source

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis

Open Mathematics, 2020
Given the abstract evolution equation y′(t)=Ay(t),t∈ℝ,y^{\prime} (t)=Ay(t),t\in {\mathbb{R}}, with a scalar type spectral operator A in a complex Banach space, we find conditions on A, formulated exclusively in terms of the location of its spectrum in ...
Markin Marat V.
doaj   +1 more source

Integral mean estimates for the polar derivative of polynomials whose zeros are within a circle

Journal of Inequalities and Applications, 2013
For a polynomial p(z) of degree n, having all zeros in |z|≤k, where k≤1, Dewan et al. (Southeast Asian Bull. Math. 34:69-77, 2010) proved that for every α∈C with |α|≥k and for each r>0, n(|α|−k){∫02π|p(eiθ)|rdθ}1r≤{∫02π|1+keiθ|rdθ}1rmax|z|=1|Dαp(z ...
A. Zireh, E. Khojastehnezhad, S. R. Musawi   +2 more
semanticscholar   +2 more sources

Inequalities for the Polar Derivative of a Polynomial [PDF]

, 2009
In this paper we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Shah [An integral mean estimate for polynomial, Indian J.
Bidkham, M., Gordji, M. Eshaghi, Shakeri, M.   +2 more
core   +4 more sources

Results on analytic functions defined by Laplace-Stieltjes transforms with perfect ϕ-type

Open Mathematics, 2020
In this paper, we introduce the concept of the perfect ϕ\phi -type to describe the growth of the maximal molecule of Laplace-Stieltjes transform by using the more general function than the usual.
Liu Simin, Xu Hongyan, Cui Yongqin, Gong Pan   +3 more
doaj   +1 more source

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis

Open Mathematics, 2019
Given the abstract evolution ...
Markin Marat V.
doaj   +1 more source