Results 221 to 230 of about 54,600 (268)
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Aequationes mathematicae, 2012
Let \(I\) be an open real interval and \(\mathcal{S}\) be a nonempty subset of all increasing bijections of \(I\) and \(\lambda:\mathcal{S}\rightarrow\mathbb R\). The authors investigate the functional equation \[ \phi\bigl(f(x)\bigr)=\phi(x)+\lambda(f)\qquad(f\in\mathcal{S},x\in I) \] in the case when the group \(G\) generated by \(\mathcal{S}\) is ...
Farzadfard, Hojjat, Robati, B. Khani
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Let \(I\) be an open real interval and \(\mathcal{S}\) be a nonempty subset of all increasing bijections of \(I\) and \(\lambda:\mathcal{S}\rightarrow\mathbb R\). The authors investigate the functional equation \[ \phi\bigl(f(x)\bigr)=\phi(x)+\lambda(f)\qquad(f\in\mathcal{S},x\in I) \] in the case when the group \(G\) generated by \(\mathcal{S}\) is ...
Farzadfard, Hojjat, Robati, B. Khani
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Systems of Generalized Abel Equations
SIAM Journal on Mathematical Analysis, 1979Certain mixed boundary value problems arising in the classical theory of elasticity lead to the solution of certain systems of generalized Abel integral equgtions. A method is presented where these systems are reduced to uncoupled pairs of Riemann boundary value problems. Closed form solutions are obtained.
Lowengrub, M., Walton, J.
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Regularisation of Abel's integral equation
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1987SynopsisConsider the Abel integral operatorwhere 0 < α < 1. Supposeuis inH1(0, 1) ofH1-norm ≦E, andfis an element ofL2(0, 1) such that ∥Au–f∥L−2< ε. We give a regularised approximate solutionuβ(f) of the equationwhich satisfiesand can be computed simply by performing some integrations.
Dang Dinh Hai, Dang Dinh Ang
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2003
Generalized Abel equations have the form $$ \phi \left( {F\left( x \right)} \right) = g\left( {x,\phi \left( x \right)} \right) $$ (3.0.1) where F : M → M is a given mapping, g(x, y) is a given function of x ∈ M, y∈ℝ and φ(x) is a solution. The Abel, Schroder and cohomological equations are particular cases of (3.0.1).
Genrich Belitskii, Vadim Tkachenko
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Generalized Abel equations have the form $$ \phi \left( {F\left( x \right)} \right) = g\left( {x,\phi \left( x \right)} \right) $$ (3.0.1) where F : M → M is a given mapping, g(x, y) is a given function of x ∈ M, y∈ℝ and φ(x) is a solution. The Abel, Schroder and cohomological equations are particular cases of (3.0.1).
Genrich Belitskii, Vadim Tkachenko
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Interval Abel integral equation
Soft Computing, 2016The authors study the solvability of the interval Abel integral equation of the form: \[ \frac{1}{\Gamma(\alpha)} \int\limits_a^t (t-s)^{\alpha-1} X(s) \text{d}s = Y(t) ,\, t \in [a, b] \tag{1} \] where \(\alpha \in (0, 1)\), \(K\) is the set of any nonempty compact intervals of the real line \(\mathbb{R}\), \(Y(\cdot) : [a, b] \to K\) being a given ...
Lupulescu, Vasile, Van Hoa, Ngo
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1990
Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. After an initial survey of Abel integral equations, this chapter focuses on the numerical solution of these equations when the ...
R. S. Anderssen, F. R. Hoog
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Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. After an initial survey of Abel integral equations, this chapter focuses on the numerical solution of these equations when the ...
R. S. Anderssen, F. R. Hoog
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Stability Results for Abel Equation
1985The author presents some estimates of solutions to Abel type integral equations. The problem of solving an Abel type integral equation is an ill-posed problem in the sense of Hadamard. The author uses these estimates to restore the stability of solutions whose first-order or fractional derivative is a priori bounded in \(L^ p\).
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Algorithmic solution of Abel’s equation
Computing, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2012
In this chapter we study the structure of the set of curves M associated with real polynomials of degree n by means of the Chebyshev correspondence.
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In this chapter we study the structure of the set of curves M associated with real polynomials of degree n by means of the Chebyshev correspondence.
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