We study the existence and shape preserving properties of a generalized Bernstein operator Bn fixing a strictly positive function f0, and a second function f1 such that f1/f0 is strictly increasing, within the framework of extended Chebyshev spaces Un. The first main result gives an inductive criterion for existence: suppose there exists a Bernstein operator Bn : C[a, b] → Un with strictly incr...

Newton-Krylov methods, primarily using the Jacobian-Free Newton-Krylov (JFNK) approximation, are examined as an alternative to the traditional power iteration method for the calculation of the fundamental eigenmode in reactor analysis applications based on diffusion theory. One JFNK approach can be considered an acceleration technique for the standard power iteration as it is “wrapped around” t...

Keywords: Set-valued mapping Chebyshev center Uniformly convex Locally uniformly convex Chebyshev fixed point a b s t r a c t The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and th...

In this paper, we consider an approach based on the elementary matrix theory. other words, take into account generalized Gaussian Fibonacci numbers. context, a general tridiagonal family. Then, obtain determinants of family via Chebyshev polynomials. Moreover, one type matrix, whose are Horadam hybrid polynomials, i.e., most form its by means polynomials second kind. We provided several illustr...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...