Uniform andLpapproximation for generalized integral polynomials

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Uniform Asymptotics for Orthogonal Polynomials

We consider asymptotics of orthogonal polynomials with respect to a weight e ?Q(x) dx on R, where either Q(x) is a polynomial of even order with positive leading coeecient, or Q(x) = NV (x), where V (x) is real analytic on R and grows suuciently rapidly as jxj ! 1. We formulate the orthogonal polynomial problem as a Riemann-Hilbert problem following the work of Fokas, Its and Kitaev. We employ ...

Integral inequalities for algebraic polynomials

In this paper we consider two extremal problems for algebraic polynomials in L 2 metrics. (1) Let Pn be the class of all algebraic polynomials P(x) = akxk of degree at most nand IJPllda= (fIR IP(x)1 2 da(x))1/2, where da(x) is a nonnegative measure on lit We determine the best constant in the inequality lakl:::; Cn,k(da)IJPl!da-, for k = O,l, ... ,n, when P E Pn and such that = 0, k = 1, ... ,m...

Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.

Generalized numerical ranges of matrix polynomials

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.