our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

An iterative algorithm is presented for solving the extended Sylvester-conjugate matrix equation. By this iterativemethod, the solvability of thematrix equation can be determined automatically. When the matrix equation is consistent, a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a mo...

A 2 XB 2 = C 2 , there are some valuable efforts on solving a pair of the matrix equations with certain linear constraints on solution. For instance, Khatri and Mitra [7] derived the Hermitian solution of the consistent matrix equations AX = C, XB = D. Deng et al. [8] studied the consistent conditions and the general expressions about the Hermitian solutions of the matrix equations (AX,XB) = (C...

In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss’s method with those obtained by some higher-order iterative methods for solving nonlinear equations. The original problem of the determination of the preliminary orbits was posed by means of a nonlinear equation. We modify this equation i...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

In this communication we give the following corrigendum for the paper ‘‘Strong convergence of the modified Ishikawa iterativemethod for infinitelymany nonexpansivemappings in Banach spaces’’ [Comput. Math. Appl. 59 (2010) 1473–1483, doi: 10.1016/j.camwa.2010.01.025]: The conditions (ii) in Theorem3.1 should be revised to 0 < lim infn→∞ βn ≤ lim supn→∞ βn < 1 and (γn(1+βn)−2βn) > a for some a ∈ ...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...