The Characterization of Solutions of $\nabla ^2 \phi + \lambda ^2 \phi = 0$ by a Functional Equation

1976 ◽  
Vol 7 (2) ◽  
pp. 271-275
Author(s):  
A. McD. Mercer
Keyword(s):  
Functional Equation ◽  
Characterization Of Solutions

scholarly journals Some results concerning the Cauchy functional equation in certain Banach algebras

1985 ◽  
Vol 31 (1) ◽  
pp. 137-144 ◽  
Author(s):  
J. Vukman
Keyword(s):  
Functional Equation ◽  
Hilbert Space ◽  
Identity Element ◽  
Banach Algebras ◽  
Cauchy Functional Equation

In this paper some results concerning the Cauchy functional equation, that is the functional equation f(x+y) = f(x) + f(y) in complex hermitian Banach *-algebras with an identity element are presented. As an application a generalization of Kurepa's extension of the Jordan-Neumann characterization of pre-Hilbert space is obtained.

Lifetime regression models based on a functional equation of physical nature

1987 ◽  
Vol 24 (01) ◽  
pp. 160-169 ◽  
Author(s):  
Enrique Castillo ◽  
Janos Galambos
Keyword(s):  
Functional Equation ◽  
Conditional Distribution ◽  
Regression Models ◽  
Practical Problem ◽  
Ad Hoc ◽  
Physical Nature ◽  
Value Theory ◽  
Complete Characterization ◽  
Lifetime Data

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.

scholarly journals On discrete algebraic Riccati equations: A rank characterization of solutions

2017 ◽  
Vol 527 ◽  
pp. 184-215 ◽  
Author(s):  
A. Sanand Amita Dilip ◽  
Harish K. Pillai ◽  
Raphaël M. Jungers
Keyword(s):  
Riccati Equations ◽  
Algebraic Riccati Equations ◽  
Characterization Of Solutions

scholarly journals Existence and Characterization of Solutions of Nonlinear Volterra-Stieltjes Integral Equations in Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Józef Banaś
Keyword(s):  
Integral Equations ◽  
Nonlinear Integral Equation ◽  
Existence Of Solutions ◽  
Stieltjes Integral ◽  
Basic Tool ◽  
Measures Of Noncompactness ◽  
Characterization Of Solutions ◽  
Fractional Orders ◽  
Stieltjes Type

The paper is devoted mainly to the study of the existence of solutions depending on two variables of a nonlinear integral equation of Volterra-Stieltjes type. The basic tool used in investigations is the technique of measures of noncompactness and Darbo’s fixed point theorem. The results obtained in the paper are applicable, in a particular case, to the nonlinear partial integral equations of fractional orders.

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