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Full-Text Articles in Physical Sciences and Mathematics
Stability Of Cauchy's Equation On Δ+., Holden Wells
Stability Of Cauchy's Equation On Δ+., Holden Wells
Electronic Theses and Dissertations
The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …
Complex Powers Of I Satisfying The Continued Fraction Functional Equation Over The Gaussian Integers, Matthew Niemiro '20
Complex Powers Of I Satisfying The Continued Fraction Functional Equation Over The Gaussian Integers, Matthew Niemiro '20
Exemplary Student Work
We investigate and then state the conditions under which iz satisfies the simple continued fraction functional equation for real and then complex z over the Gaussian integers.
Functional Equations With Involution Related To Sine And Cosine Functions., Allison Perkins
Functional Equations With Involution Related To Sine And Cosine Functions., Allison Perkins
Electronic Theses and Dissertations
Let G be an abelian group, C be the _eld of complex numbers, _ 2 G be any _xed, nonzero element and _ : G ! G be an involution. In Chapter 2, we determine the general solution f; g : G ! C of the functional equation f(x + _y + _) + g(x + y + _) = 2f(x)f(y) for all x; y 2 G. Let G be an arbitrary group, z0 be any _xed, nonzero element in the center Z(G) of the group G, and _ : G ! G be an involution. The main goals of …
An Iterated Pseudospectral Method For Functional Partial Differential Equations, J. Mead, B. Zubik-Kowal
An Iterated Pseudospectral Method For Functional Partial Differential Equations, J. Mead, B. Zubik-Kowal
Jodi Mead
Chebyshev pseudospectral spatial discretization preconditioned by the Kosloff and Tal-Ezer transformation [10] is applied to hyperbolic and parabolic functional equations. A Jacobi waveform relaxation method is then applied to the resulting semi-discrete functional systems, and the result is a simple system of ordinary differential equations d/dtUk+1(t) = MαUk+1(t)+f(t,U kt). Here Mα is a diagonal matrix, k is the index of waveform relaxation iterations, U kt is a functional argument computed from the previous iterate and the function f, like the matrix Mα, depends on the process of semi-discretization. This waveform relaxation splitting has the advantage of straight forward, direct application …
An Iterated Pseudospectral Method For Functional Partial Differential Equations, J. Mead, B. Zubik-Kowal
An Iterated Pseudospectral Method For Functional Partial Differential Equations, J. Mead, B. Zubik-Kowal
Mathematics Faculty Publications and Presentations
Chebyshev pseudospectral spatial discretization preconditioned by the Kosloff and Tal-Ezer transformation [10] is applied to hyperbolic and parabolic functional equations. A Jacobi waveform relaxation method is then applied to the resulting semi-discrete functional systems, and the result is a simple system of ordinary differential equations d/dtUk+1(t) = MαUk+1(t)+f(t,U kt). Here Mα is a diagonal matrix, k is the index of waveform relaxation iterations, U kt is a functional argument computed from the previous iterate and the function f …
Existence Of Solutions For Discontinuous Functional Equations And Elliptic Boundary-Value Problems, Siegfried Carl, Seppo V. Heikkilä
Existence Of Solutions For Discontinuous Functional Equations And Elliptic Boundary-Value Problems, Siegfried Carl, Seppo V. Heikkilä
Mathematics and System Engineering Faculty Publications
We prove existence results for discontinuous functional equations in general Lp-spaces and apply these results to the solvability of implicit and explicit elliptic boundary-value problems involving discontinuous nonlinearities. The main tool in the proof is a fixed point result in lattice-ordered Banach spaces proved by the second author. © 2002 Southwest Texas State University.
On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic
On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
It is shown that the method used by C. V. Stanojevic to obtain a characterization of inner product spaces in terms of a Mielnik probability space of dimension 2 does not admit a generalization to dimension n > 2. © 1975 American Mathematical Society.
Existence And Continuous Dependence For A Class Of Nonlinear Neutraldifferential Equations, L. J. Grimm
Existence And Continuous Dependence For A Class Of Nonlinear Neutraldifferential Equations, L. J. Grimm
Mathematics and Statistics Faculty Research & Creative Works
This paper presents existence, uniqueness, and continuous dependence theorems for solutions of initial-value problems for neutral-differential equations of the form (equation omited), where f, g, and h are continuous functions with g(0, x0)=h(0, x0) = 0. The existence of a continuous solution of the functional equation z(t) =f(t, z(h(t))) is proved as a corollary. © 1971 American Mathematical Society.