By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

This paper describes the interpolation of head related transfer functions (HRTFs) for all directions. The interpolation of HRTFs enables us to reduce the number of measurements for new user’s HRTFs, and also reduce the data of HRTFs in auditory virtual systems. A linear interpolation and the spline interpolation are evaluated and the advantages of both methods are clarified. The interpolation m...

Using recent results where we constructed refinable functions for composite dilations, we construct interpolating multiscale decompositions for such systems. Interpolating wavelets are a well-known construction similar to the usual L2-theory but with L2-projectors onto the scaling spaces replaced by L∞projectors defined by an interpolation procedure. A remarkable result is that this much simple...

A dilation equation is a functional equation of the form f (t) = N k=0 c k f (2t − k), and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Hölder exponent of continuity of any continuous, compactly supported s...

We build discrete-time compactly supported biorthogonal wavelets and perfect reconstruction filter banks for any lattice in any dimension with any number of primal and dual vanishing moments. The associated scaling functions are interpolating. Our construction relies on the lifting scheme and inherits all of its advantages: fast transform, in-place calculation, and integer-to-integer transforms...

Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the order of the underlying interpolating polynomial that is used to generate IS...

We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the representation, we construct a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions. The wavelets in these biorthogonal pairs have properties better suited for curves and surfaces than many commonly used lters. We also give example...