American Journal of Applied Mathematics and Statistics

This paper surveys and reviews paper of spline degree seven inhomogeneous and optimized the best errors bound by spline (0,2, 5; 0, 3, 6) case. It has been shown that the existence, uniqueness and convergence analysis with minimizing the error bounds of deficient seventh spline interpolated.

American Journal of Applied Mathematics and Statistics. 2013, 1(3), 46-51. DOI: 10.12691/ajams-1-3-3
Pub. Date: June 18, 2013

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Existence and Uniqueness Theorem for Set-Valued Volterra Integral Equations

by Andrej V. Plotnikov and Natalia V. Skripnik

Original Research

The space of nonempty compact sets of

is well-known to be a nonlinear space. This fact essentially complicates the research of set-valued differential and integral equations. In this article we consider set-valued Volterra integral equations and prove the existence and uniqueness theorem.

American Journal of Applied Mathematics and Statistics. 2013, 1(3), 41-45. DOI: 10.12691/ajams-1-3-2
Pub. Date: May 19, 2013

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Frames from Cosines with the Degenerate Coefficients

by Sadigova Sabina Rahib and Mamedova Zahira Vahid

Original Research

The system of cosines with a degenerate coefficient in exponential form is considered. A necessary and sufficient condition on the degree of degeneration is found that makes the considered system a frame in Lebesgue spaces. It is proved that if the degenerate coefficient satisfies the Muckenhoupt condition, then the basicity holds. If the Muckenhoupt condition does not hold, then the system has a finite defect, and does not form a frame.

American Journal of Applied Mathematics and Statistics. 2013, 1(3), 36-40. DOI: 10.12691/ajams-1-3-1
Pub. Date: May 17, 2013

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