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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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