• Title/Summary/Keyword: Entire function

Search Result 776, Processing Time 0.02 seconds

AN ENTIRE FUNCTION SHARING A POLYNOMIAL WITH LINEAR DIFFERENTIAL POLYNOMIALS

  • Ghosh, Goutam Kumar
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.2
    • /
    • pp.495-505
    • /
    • 2018
  • The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_1(z)f^{(1)}(z)+a_2(z)f^{(2)}(z)+{\cdots}+a_n(z)f^{(n)}(z)$, where the coefficients $a_k(z)(k=1,2,{\ldots},n)$ are rational functions and $a_n(z){\not{\equiv}}0$.

FEW RESULTS IN CONNECTION WITH SUM AND PRODUCT THEOREMS OF RELATIVE (p, q)-𝜑 ORDER, RELATIVE (p, q)-𝜑 TYPE AND RELATIVE (p, q)-𝜑 WEAK TYPE OF MEROMORPHIC FUNCTIONS WITH RESPECT TO ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • The Pure and Applied Mathematics
    • /
    • v.26 no.4
    • /
    • pp.315-353
    • /
    • 2019
  • Orders and types of entire and meromorphic functions have been actively investigated by many authors. In the present paper, we aim at investigating some basic properties in connection with sum and product of relative (p, q)-𝜑 order, relative (p, q)-𝜑 type, and relative (p, q)-𝜑 weak type of meromorphic functions with respect to entire functions where p, q are any two positive integers and 𝜑 : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

Set shared by an Entire Function with its k-th Derivative Using Normal Families

  • Ahamed, Molla Basir
    • Kyungpook Mathematical Journal
    • /
    • v.60 no.2
    • /
    • pp.387-399
    • /
    • 2020
  • In this paper, we study a problem of a non-constant entire function f that shares a set S = {a, b, c} with its k-th derivative f(k), where a, b and c are any three distinct complex numbers. We have found a gap in the statement of the main result of Chang-Fang-Zalcman [10], and with the help of their method, we have generalize their result in a more compact form. As an application, we generalize the famous Brück conjecture [9] with the idea of set sharing.

SOME GROWTH ASPECTS OF SPECIAL TYPE OF DIFFERENTIAL POLYNOMIAL GENERATED BY ENTIRE AND MEROMORPHIC FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH ORDERS

  • Biswas, Tanmay
    • Korean Journal of Mathematics
    • /
    • v.27 no.4
    • /
    • pp.899-927
    • /
    • 2019
  • In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

VALUE DISTRIBUTION OF SOME q-DIFFERENCE POLYNOMIALS

  • Xu, Na;Zhong, Chun-Ping
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.1
    • /
    • pp.29-38
    • /
    • 2016
  • For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

EFFECT OF INTEGER TRANSLATION ON RELATIVE ORDER AND RELATIVE TYPE OF ENTIRE AND MEROMORPHIC FUNCTIONS

  • Biswas, Tanmay;Datta, Sanjib Kumar
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.2
    • /
    • pp.485-494
    • /
    • 2018
  • In this paper some newly developed results based on the growth properties of relative order (relative lower order), relative type (relative lower type) and relative weak type of entire and meromorphic functions on the basis of integer translation applied upon them are investigated.

ON SOME GROWTH ANALYSIS OF COMPOSITE ENTIRE AND MEROMORPHIC FUNCTIONS FROM THE VIEW POINT OF THEIR RELATIVE (p, q)-TH TYPE AND RELATIVE (p, q)-TH WEAK TYPE

  • Biswas, Tanmay
    • Korean Journal of Mathematics
    • /
    • v.26 no.1
    • /
    • pp.23-41
    • /
    • 2018
  • The main aim of this paper is to prove some results related to the growth rates of composite entire and meromorphic functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type and relative (p, q)-th weak type where p and q are any two positive integers.

GROWTH OF SOLUTIONS TO LINEAR DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS OF [p, q]-ORDER IN THE COMPLEX PLANE

  • Biswas, Nityagopal;Tamang, Samten
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.4
    • /
    • pp.1217-1227
    • /
    • 2018
  • In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.

RELATIVE (p, q)-𝜑 ORDER AND RELATIVE (p, q)-𝜑 TYPE ORIENTED GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • Honam Mathematical Journal
    • /
    • v.41 no.2
    • /
    • pp.243-268
    • /
    • 2019
  • The main aim of this paper is to study some growth properties of composite entire functions on the basis of relative $(p,q)-{\varphi}$ type and relative $(p,q)-{\varphi}$ weak type where p and q are any two positive integers and ${\varphi}(r):[0,+{\infty}){\rightarrow}(0,+{\infty})$ be a non-decreasing unbounded function.