An inverse function theorem via continuous Newton’s method

An inverse function theorem in Fréchet spaces

I present an inverse function theorem for differentiable maps between Fréchet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue’s dominated convergence theorem and Ekeland’s variational principle. As a consequence, the assumptions are substantially weakened: th...

Newtons levitation theorem and photoacoustic integral geometry

Two subjects are addressed. A series of mass distributions is explicitly presented, that generate zero gravitation …eld in an open set in E. Second, an explicit reconstruction formula in E from data of spherical means with centers in an algebraic set. For both constructions, the same geometric method is applied based on properties of a special class of polynomials. Key words oscillatory set hyp...

On the Inverse Function Theorem

Numerical Method for Three-parameter Eigenvalue Problems using Newtons method based on Trace Theorem

Atkinson, F. V. ,1972. 'Multiparameter Eigenvalue Problems', (Matrices and compact operators) Academic Press, New York, Vol. 1 Atkinson, F. V. , 1968. 'Multiparameter spectral theory', Bull. Am. Math. Soc. , Vol. 75, pp(1-28) Baruah, A. K. , 1987. 'Estimation of eigen elements in a two-parameter eigen value problem', Ph. D Thesis, Dibrugarh University, Assam. Bindi...

Banach's Continuous Inverse Theorem and Closed Graph Theorem

The terminology and notation used here have been introduced in the following articles: [3], [4], [2], [15], [11], [14], [1], [5], [13], [12], [19], [20], [16], [7], [17], [8], [18], [9], and [6]. Let X, Y be non empty normed structures, let x be a point of X, and let y be a point of Y . Then 〈x, y〉 is a point of X × Y. Let X, Y be non empty normed structures, let s1 be a sequence of X, and let ...