*FOURIER analysis, *MATHEMATICS, *POUSSINISTS, *MODULUS of rigidity, *ARITHMETIC
Abstract
In this paper, we consider norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series for the Walsh system. We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. [ABSTRACT FROM AUTHOR]
In this paper, we study the following two-dimesional system of difference equations ... where the parameters a;b; c;d and the initial values x i; y i, i 2 f1;2;3;4;5;6g, are real numbers. We show that some subclasses of nonlinear two-dimensional system of difference equations are solvable in closed form. We also describe the forbidden set of solutions of the system of differ- ence equations. Some numerical examples are given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]
In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of several double inequalities for bounding Neuman-Sándor means in terms of the arithmetic, harmonic, and contra-harmonic means and discover some new sharp inequalities involving Neuman-Sándor, contra-harmonic, root-square, and other means of two positive real numbers. [ABSTRACT FROM AUTHOR]
In this paper we are dealing with the problem of the existence of two divisors of .(n2+1)/2 whose sum is equal to δn+ε, in the case when δ and εn+ε are even, or more precisely in the case in which δ ≡ εn+2 ≡ 0 or 2 .mod 42. We will completely solve the cases δ=2,δ δ=4 andε = 0. [ABSTRACT FROM AUTHOR]
Let Mn be the algebra of all n × n matrices with entries in the field of real numbers. For a matrix Z ∊ Mn, it is said that a linear map T : Mn →Mn is multiplicative at Z if T (AB) = T (A)T (B) whenever AB = Z. In this paper we investigate some properties of multiplicative mapping at invertible matrices and also we characterize all multiplicative isomorphisms at invertible matrices. Then we give an example to show that multiplicativity at I doesn't imply multiplicativity on Mn, where I ∊ Mn is the identity matrix. [ABSTRACT FROM AUTHOR]