WEIGHTED SHARING OF ENTIRE FUNCTIONS CONCERNING LINEAR DIFFERENCE OPERATORS | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 12, Issue 2, 2024, Pages 1-10 PDF (220.71 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2024.270077.1129 | ||
| Author | ||
| Megha M Manakame* | ||
| Bangalore university Bangalore | ||
| Abstract | ||
| In this research article, we investigates the value distribution of linear q-di erence operators Lk(f;q;c) and Lk(g;q;c), for a transcendental entire functions of zero order. At the same time we also investigate the uniqueness problems when two linear q- di erence operators of entire functions share one value with nite weight. Our results extends the previous theorems of existing studies [11],[5]. In this paper, we assume that the reader is familiar with the fundamental results [7],[14],[15]. We adopt the standard notations of the Nevanlinna theory of meromorphic function m(r; f), N(r; f), N(r; 0; f) and T(r; f) denote the proximity function, the counting function, the reduced counting function and the characteristic function of f(z), respectively. Let f and g be two non-constant meromorphic functions de ned in the complex plane and S(r; f) denote any quantity satisfying S(r; f) = o(T(r; f)) as r ! 1 possibly exceptional set of nite linear measure. A meromorphic function (6 0;1) is called a small function with respect to f, if T(r; ) = S(r; f). If for some a 2 C [1, the zeros of f a and g a coincide in locations and multiplicity, we say that f and g share the value a CM(Counting Multiplicities). On the other hand, if the zeros of f a and g a coincide only in their locations, then we say that f and g share the value a IM(Ignoring Multiplicities). | ||
| Keywords | ||
| Entire functions; Linear Difference operator; Weighted sharing; Uniqueness | ||
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