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On Reverse Triangle Inequality and Some of Its Applications

Author

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  • Ivan D. Arand-elović

    (University of Belgrade - Faculty of Mechanical Engineering)

Abstract

In Euclidean space, the triangle inequality asserts that the sum of any two sides of a triangle is strictly bigger than the remaining third side. The reverse triangle inequality is its equivalent, which says that any side of a triangle is strictly greater than the difference between the other two sides. In first part of this chapter, we shall prove equivalence of triangle inequality and reverse triangle inequality on class of pseudometric spaces. Further, as examples of applications of reverse triangle inequality, we shall prove one generalization of an inequality of D. D. Adamović (see [D. S. Mitrinović (in cooperation with P. M. Vasić), Analytic Inequalities, Springer-Verlag, Berlin, Heidelberg 1970.] page 281) and two partial infinite-dimensional generalizations of an inequality obtained by G. V. Milovanović and I. Ž. Milovanović [A generalization of a problem given by D. S. Mitrinović, Publ. Elektroteh. Fak., Univ. Beogr., Ser. Mat. Fiz. 602–633, 129–132.].

Suggested Citation

  • Ivan D. Arand-elović, 2025. "On Reverse Triangle Inequality and Some of Its Applications," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-85743-0_6
    DOI: 10.1007/978-3-031-85743-0_6
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