Dubinin, V. N. The Schwarz inequality on the boundary for functions regular in the disk. (English. Russian original) Zbl 1070.30008 J. Math. Sci., New York 122, No. 6, 3623-3629 (2004); translation from Zap. Nauchn. Semin. POMI 286, 74-84 (2002). Summary: The classical Schwarz inequality on the boundary of the disk for the functions regular in the disk is refined in various directions. Inequalities involving zeros of the function, an inequality for points mapped to symmetric points on the circle, and an inverse estimate for univalent functions are presented. Other inequalities are discussed, and the possibility of applying them to estimates of polynomials and rational functions is indicated. Cited in 1 ReviewCited in 50 Documents MSC: 30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination × Cite Format Result Cite Review PDF Full Text: DOI