The Generalized Pomeron Functional Equation. (25th December 2019)

• Record Type: Journal Article
• Authors: Shi, Yong-Guo
• Other Names: Anderson Douglas R. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2019(2019)
• Publication Date: 2019-12-25
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2019/6903908
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : This paper investigates the linear functional equation with constant coefficients φ t = κ φ λ t + f t, where both κ > 0 and 1 > λ > 0 are constants, f is a given continuous function on ℝ, and φ : ℝ ⟶ ℝ is unknown. We present all continuous solutions of this functional equation. We show that (i) if κ > 1, then the equation has infinite many continuous solutions, which depends on arbitrary functions; (ii) if 0 < κ < 1, then the equation has a unique continuous solution; and (iii) if κ = 1, then the equation has a continuous solution depending on a single parameter φ 0 under a suitable condition on f .