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The techniques that will be used in the proofs are mainly based on classical real analysis, especially on the well-known Hölder's inequality and on Fubini's theorem.
The techniques that we use in the paper are based on classical real analysis and the application of the Abel-Gontscharoff interpolation.
The methods used are based on classical real analysis and the application of Lidstone's interpolating polynomials and exponential convexity method and can be extended to the investigation of other inequalities.
This section is intended to illustrate the contribution of the quaternionic wavelet transform, the multiband information in spectral and spatial thresholding, and the phase smoothing compared to the methods based on classical real neighboring coefficient regularization.
Moreover, the obtained generalizations represent an extension to real, not necessarily nonnegative entries of the vectors a, b, and the matrix A. The methods used are based on classical real analysis and the application of the Abel-Gontscharoff formula and Green's function and can be extended to the investigation of other inequalities.
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