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Explicit forms of invariant means: complementary results to Gauss $$\left( {\mathcal {A}},{\mathcal {G}}\right) $$-theorem and some applications
Abstract Explicit forms of invariant means for all mean-type mappings generated by the bivariable classical arithmetic, geometric and harmonic means (complementary to the Gauss $$\mathcal {AGM}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>AGM</mml:mi> </mml:math> -theorem) are given. A generalization for higher dimension mean-type mappings as well as two open problems and an application in …