Limiting value of lower indicator and lower bound for entire functions with positive zeros

1972 ◽  
Vol 24 (4) ◽  
pp. 390-395 ◽  
Author(s):  
A. A. Kondratyuk ◽  
A. N. Fridman

1991 ◽  
Vol 11 (4) ◽  
pp. 769-777 ◽  
Author(s):  
Gwyneth M. Stallard

AbstractWe construct a set of transcendental entire functions such that the Hausdorff dimensions of the Julia sets of these functions have greatest lower bound equal to one.



2021 ◽  
Vol 7 (1) ◽  
pp. 276-287
Author(s):  
Zheng Wang ◽  
◽  
Zhi Gang Huang

<abstract><p>This paper is devoted to studying the transcendental directions of entire solutions of $ f^{(n)}+A_{n-1}f^{(n-1)}+...+A_0f = 0 $, where $ n(\geq 2) $ is an integer and $ A_i(z)(i = 0, 1, ..., n-1) $ are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.</p></abstract>



2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianren Long ◽  
Chunhui Qiu ◽  
Pengcheng Wu

We consider that the linear differential equationsf(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0, whereAj  (j=0,1,…,k-1), are entire functions. Assume that there existsl∈{1,2,…,k-1}, such thatAlis extremal forYang'sinequality; then we will give some conditions on other coefficients which can guarantee that every solutionf(≢0)of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder offif every solutionf(≢0)of the equation is of infinite order.



1990 ◽  
Vol 48 (5) ◽  
pp. 613-615
Author(s):  
B. G. Freidin
Keyword(s):  


2018 ◽  
Vol 48 (1) ◽  
pp. 33-45
Author(s):  
Goutam Kumar Ghosh


2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.



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