On the discrete extension of Markov's theorem on monotonicity of zeros (Q896874)

In 1989 an open problem has been proposed in [\textit{M. E. H. Ismail}, IMA Vol. Math. Appl. 18, 177--190 (1989; Zbl 0698.33008)], concerning the behavior of zeros of orthogonal polynomials associated with a measure given by \(w(x,r)dx+dv(x,r)\), where \(v(.,r)\) is a jump function or a step function. In this article the authors solve a particular case of the open problem, based on the theory of spectral transformations of orthogonal polynomials. Almost at the same period it was also proved in another way in ref. [\textit{D. K. Dimitrov}, ``Monotonicity of zeros of polynomials orthogonal with respect to a discrete measure'', \url{arXiv:1501.07235}].