On the existence and uniqueness of analytic solutions of a linear functional equation

1967 ◽  
Vol 98 (3) ◽  
pp. 235-242 ◽  
Author(s):  
A. Smajdor ◽  
W. Smajdor
Keyword(s):  
Functional Equation ◽  
Existence And Uniqueness ◽  
Linear Functional ◽  
Analytic Solutions ◽  
Linear Functional Equation

scholarly journals Series Solution of a Functional Equation

1965 ◽  
Vol 5 (1) ◽  
pp. 48-55
Author(s):  
W. Pranger
Keyword(s):  
Functional Equation ◽  
Linear Operator ◽  
Operator Theory ◽  
Inversion Formula ◽  
Linear Functional ◽  
Series Solution ◽  
Analytic Solutions ◽  
Linear Functional Equation ◽  
General Operator ◽  
Image Position

In this we will study analytic solutions to the linear functional equation where f and h are given functions, x is a given complex number and the function g is to be found. This is a generalization of Schröder's functional equation. The results obtained are global in nature and the solutions holomorphic. The equation will be viewed from the standpoint of linear operator theory. When studied in this manner one arrives at a general operator inversion formula.

scholarly journals Regularly varying solutions of a linear functional equation

1976 ◽  
Vol 22 (2) ◽  
pp. 135-143 ◽  
Author(s):  
Marek Kuczma
Keyword(s):  
Functional Equation ◽  
Existence And Uniqueness ◽  
Linear Functional ◽  
Existence Of Solutions ◽  
General Linear ◽  
Linear Functional Equation ◽  
Uniqueness Of Solutions ◽  
Regularly Varying ◽  
Image Position ◽  
The Given

AbstractWe are concerned with the problem of the existence and uniqueness of regularly varying (in Karamata's sense) solutions ϕ of the linear functional equation in a right neighbourhood of x = 0. Under suitable conditions on the given functions f and h, the uniqueness of solutions depends essentially on whether the series Σh ∘ f1 converges or diverges; here fi denotes the i-th functional iterate of f. The existence of solutions may be proved under further assumptions.The case of the more general linear functional equation may be reduced to that of equation (*).

On a linear functional equation

1989 ◽  
Vol 38 (2-3) ◽  
pp. 113-122 ◽  
Author(s):  
László Székelyhidi
Keyword(s):  
Functional Equation ◽  
Linear Functional ◽  
Linear Functional Equation

scholarly journals The Generalized Pomeron Functional Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-4
Author(s):  
Yong-Guo Shi
Keyword(s):  
Functional Equation ◽  
Continuous Function ◽  
Linear Functional ◽  
Continuous Solution ◽  
Suitable Condition ◽  
Single Parameter ◽  
Linear Functional Equation ◽  
Continuous Solutions ◽  
Constant Coefficients

This paper investigates the linear functional equation with constant coefficients φt=κφλt+ft, 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 φ0 under a suitable condition on f.

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