Abstract. This paper deals with the reverse inequalities of Erdös-Mordell type. Our result contains as special case the following reverse Erdös-Mordell inequality:where R i and ρ i (i=1, 2, 3) denote respectively the distances from an interior point Q of A 1 A 2 A 3 to the vertexes A 1 , A 2 , A 3 and to the circumcenters of A 2 QA 3 , A 3 QA 1 , A 1 QA 2 . Some other closely related inequalities are also considered.Mathematics subject classification (2000): 26D05, 26D15, 51M16.
Abstract. Hexagonal quasigroup is idempotent, medial and semisymmetric quasigroup. In this article we define and study vectors, sum of vectors and transfers. The main result is the theorem on isomorphism between the group of vectors, group of transfers and the Abelian group from the characterization theorem of the hexagonal quasigroups.
Hexagonal quasigroupHexagonal quasigroups are defined in article [3].is idempotent, medial and semisymmetric; i.e. if its elements a, b, c, d satisfyWhen it doesn't cause confusion, we can omit the sign "·", e.g. instead of (a · b) · (c · d) we shall write ab · cd. The basic example of a hexagonal quasigroup studied in [3] is the following.2000 Mathematics Subject Classification. 20N05.
In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and Hölder type functions etc. These results give us an elegant method for obtaining a number of inequalities for various kinds of fractional integral operators such as for the Riemann-Liouville fractional integral operator, the Hadamard fractional integral operator, fractional hyperqeometric integral and corresponding q-integrals.1991 Mathematics Subject Classification. 26D10; 26A33. Key words and phrases. the Chebyshev inequality, the Chebyshev difference, fractional integral operator, isotonic linear functional, Lipschitz function.
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