Markov, A. A., Ob odnom voproce D. I. Mendeleeva, Zapiski Imperatorskoi Akademii Nauk SP6. 62 (1890), 1-24. This is the original paper in Old Russian spelling (and we thank V. V. Arestov and Elena Berdysheva for providing this copy). This paper contains the proof of the Markov inequality for algebraic polynomials. This journal was later called Mémoires de l'Academie Impériale des Sciences de St.-Pétersbourg VIe séries. Due, it seems, to translating the name of the journal into French and then back into Russian, many sources now reference this article as being in Izv. Petersburg Acad. Nauk or some variant thereof. As such it was referenced (and also with the year 1889) in A. A. Markov's Selected Works from 1948 which contains a transcription of the above paper into modern Russian spelling. We also have an English translation On a question by D. I. Mendeleev prepared by Carl de Boor and Olga Holtz.

This letter from Heinz-Joachim Rack provides an extended discussion of the effects on Approximation Theory and Analysis of Mendeleev's question as well as of the relevant parts of Mendeleev's book. Here , thanks to Heinz-Joachim Rack, are the most relevant pages, page 289 and page 290, of Mendeleev's book. To be sure, these pages use the old Russian spelling.

Boas, R. P., Extremal problems for polynomials, Amer. Math. Monthly 85 (1978), 473-475. A short pleasant expository note about the origins of the Markov inequality. This article may be viewed electronically at JSTOR

The article The life and work of A.A. Markov by Gely P. Basharin, Amy N.Langville and Valeriy A Naumov, Linear Algebra and its Applications 386 (2004) 3--26, should be read with some caution, according to its review in Zentralblatt Math. For those with access, this article may be viewed at Science Direct.

His son, Andrey Andreyevich Markov Jr. (1903-1979) was one of the key founders of the Russian school of constructive mathematics and logic.