Functions and differences whose roots have the same real part

Piriya Prunglerdbuathong; Kiattisak Prathom; Suton Tadee; Vichian Laohakosol

Authors

Piriya Prunglerdbuathong
Kiattisak Prathom
Suton Tadee
Vichian Laohakosol

Keywords:

entire functions, differences, zeros, real part

Abstract

Let $gif.latex?f&space;:&space;\mathbb{C}&space;\rightarrow&space;\mathbb{C}$ be an entire function of order $gif.latex?\leq&space;1$ . Assume that all the roots of $gif.latex?f$ have the same real part, abbreviated by $gif.latex?f&space;\in&space;SRP$ . For $gif.latex?\lambda&space;\in&space;\mathbb{R}\setminus&space;\{0\}$ , define $gif.latex?\Delta_{\lambda}f(z)&space;:=&space;f(z+\lambda)-f(z)$ . We investigate the situation when $gif.latex?\Delta_{\lambda}f(z)&space;\in&space;SRP$ .

Functions and differences whose roots have the same real part

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