Some Properties of Entire Functions Associated with L-entire Functions on C(I)

Roberto Contreras, Hector D. Ramirez, Nelva B. Espinoza

In this paper, let C(I) denote the Banach algebra of all continuous complex-valued functions defined on a close interval I in the set of real numbers, R. The functions having derivatives in the Lorch sense on the whole Banach algebra C(I) are considered and they are called L-entire functions [1, 3]. For each L-entire function on C(I), entire complex functions are associated and the relationship between their orders is studied. Even more, the possibility of locating the solutions of the equation F(f) = 0 from the location of zeros of the associated family of entire functions with F is analyzed too.