The first Seiffert mean is strictly (G,A)-super-stabilizable

The concept of strictly super-stabilizability for bivariate means has been defined recently by Ra\”{\i}soulli and S\'{a}ndor (J. Inequal. Appl. 2014:28,2014). We answer into affirmative to an open question posed in that paper, namely: Prove or disprove that the first Seiffert mean P~is strictly~ \[(G,A)\] -super-stabilizable. We use series expansions of the functions involved and reduce the main inequality to three auxiliary ones. The computations are performed with the aid of the computer algebra systems~Maple~and~Maxima. The method is general and can be adapted to other problems related to sub- or super-stabilizability.

Mira C Anisiu
T. Popoviciu Institute of Numerical Analysis, Romanian Academy, Fantanele 53, Cluj-Napoca, România

Valeriu Anisiu
Faculty of Mathematics and Computer Science, Babeş-Bolyai University,  Cluj-Napoca,  Romania

(pdf file here)

https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/1029-242X-2014-185

M.-C. Anisiu, V. Anisiu, The first Seiffert mean is strictly (G,A)-super-stabilizable, J. Ineq. Appl., 2014, 2014:185

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