[PDF] Top 20 Some results on entire functions that share one value with their difference operators

... have some special relationship. One of successful attempts in this direction was created by Rubel and Yang ...non-constant entire function f (z), if f (z) and f (z) share two distinct finite ... See full document

... In this paper, we consider uniqueness problems on entire functions that share a small periodic entire function with their two difference operators and obtain some results. ... See full document

... they share 3 distinct non-zero, finite values(or small functions) IM, with addi- tional conditions as ...main results, let us give some ... See full document

... between entire functions and their derivatives was first studied by Rubel and Yang ...nonconstant entire function f and its first derivative f share two distinct finite numbers a, b CM, then f ≡ ... See full document

... an entire function sharing one finite value with its ...derivatives. Some recent papers studied the case of entire functions of finite order sharing a periodic small function to f ... See full document

... of value distributions is concerned with the density of points where a meromorphic function takes a certain value in the complex ...meromorphic functions and their shifts or their difference ... See full document

... It is natural to pose the question: what can be said on replacing shared values in Theo- rems C–E by shared small functions. Concerning this question, we obtain the following results which extend Theorems ... See full document

... in value distribution of difference operators of meromorphic functions (see ...uniqueness results of difference polynomials of meromorphic functions, their shifts and ... See full document

... an entire function shares 0 CM and nonzero complex constant a IM with its difference ...they share two distinct complex constants a ∗ CM and a IM under some additional condition and give some ... See full document

... their difference operators (see, e.g., [8-13]). Some of them (see, ...two entire functions share a small ...of difference operators of meromorphic ... See full document

... transcendental entire function of finite order and α(z) be a small function with respect to f ...transcendental entire function of finite or- der and α(z) be a small function with respect to both f (z) and ... See full document

... meromorphic functions f (z) and g(z) share the value a IM (ignoring multiplicities) if f (z) – a and g(z) – a have the same ...they share the value a CM (counting ... See full document

... an entire function is equal to its difference operator if it has a growth property and shares a set, where the set consists of two entire functions of smaller ... See full document

... positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin ... See full document

... where a = ± iA, A = (–) c k kπ , k is an integer, b is a constant and p, q, c are non-zero constants. Remark . Equation (.) is a special case of (.). Theorem D generalized Theorem B. From Theorem D, we see that if ... See full document

... In [1], W. R. Derrick and L. Nova defined the following operator classes: Let (X, ∥ . ∥ ) be a Banach space, let K be a closed subset of X and let T : X → X be an arbitrary operator that satisfies one of the ... See full document

... (2) Theorem 1.1 does not remain valid when n = 1. For example, f (z) = e z + 1 and f (z + c) = e z+c + 1, where c ≠ 2 π i. Clearly, f(z) and f (z + c) share 1 and ∞ CM, however, f (z) ≠ ω f (z + c) for ω n = 1. ... See full document

... studied some growth properties of entire functions using relative ...discuss some comparative growth properties of entire and meromorphic functions in terms of their relative ... See full document

... -order pf of f be defined as the inflmu of positive numbers p such that, for sufflclently large r,.. function f, let the.[r] ... See full document

... Let f { z ) be an analytic self-map of a domain D of C . Complex dynamics studies the Fatou set, E ( / ) , which is defined as the maximal open subset of D where the iterates { f ^ } of f {z ) form a normal family. The ... See full document