Tian-Zhou Xu

A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi--Normed Spaces

We achieve the general solution of the quintic functional equation and the sextic functional equation . Moreover, we prove the stability of the quintic and sextic functional equations in quasi--normed spaces via fixed point method.

Intuitionistic fuzzy stability of a general mixed additive-cubic equation

We establish some stability results concerning the general mixed additive-cubic functional equation, f(kx+y)+f(kx−y)=kf(x+y)+kf(x−y)+2f(kx)−2kf(x),in intuitionistic fuzzy normed spaces. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.

Stability of a general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces

We establish some stability results concerning the general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces. In addition, we establish some results of approximately general mixed additive-cubic mappings in non-Archimedean fuzzy normed spaces. The results improve and extend some recent results.

A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces

Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation 𝑓(𝑥

Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided.

Symmetry properties and explicit solutions of the nonlinear time fractional KdV equation

The time fractional KdV equation in the sense of the Riemann-Liouville derivatives is considered. The symmetry properties of the time fractional KdV equation is investigated by using the Lie group analysis method. On the basis of the point symmetry, the vector fields of the time fractional KdV equation are presented. And then, the symmetry reductions are constructed. By right of the obtained Lie point symmetries, it is shown that this equation could transform into a nonlinear ordinary differential equation of fractional order with the new independent variable ξ=xt−α/3. The derivative is an Erdélyi-Kober derivative depending on a parameter α. At last, by means of the sub-equation method, some exact and explicit solutions of the time fractional KdV equation are constructed.MSC:22E70, 26A33.

Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.

Approximating bandlimited signals associated with the LCT domain from nonuniform samples at unknown locations

The sampling theory describes ways of reconstructing signals from their uniform or nonuniform samples associated with the traditional Fourier transform (FT). Most of the published papers about the sampling theory require signals to be bandlimited in the FT domain and assume that the sample locations and the band width are all known. However, the sample locations are not always known and most of the signals are non-stationary in practical applications. In order to overcome these shortcomings, this paper provides an algorithm for approximating signals from nonuniform samples at unknown locations. These signals are not necessarily bandlimited in the FT domain, however bandlimited in the LCT domain. The experimental results are given to verify the accuracy of the algorithm.

On the stability of multi-Jensen mappings in β-normed spaces

Abstract In this work, we prove the generalized Hyers–Ulam stability of the multi-Jensen mappings in β -normed spaces.

The Poisson sum formulae associated with the fractional Fourier transform

The theorem of sampling formulae has been deduced for band-limited or time-limited signals in the fractional Fourier domain by different authors. Even though the properties and applications of these formulae have been studied extensively in the literature, none of the research papers throw light on the Poisson sum formula and non-band-limited signals associated with the fractional Fourier transform (FrFT). This paper investigates the generalized pattern of Poisson sum formula from the FrFT point of view and derived several novel sum formulae associated with the FrFT. Firstly, the generalized Poisson sum formula is obtained based on the relationship of the FrFT and the Fourier transform; then some new results associated with this novel sum formula have been derived; the potential applications of these new results in estimating the bandwidth and the fractional spectrum shape of a signal in the fractional Fourier domain are also proposed. In addition, the results can be seen as the generalization of the classical results in the Fourier domain.