THE SHARPER VERSION FOR GENERALIZED POWER MEAN INEQUALITIES WITH NEGATIVE EXPONENT

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Tinaztepe R., Tınaztepe G., Eken Z., Sezer S., Kemali S., Işık İ. Y., ...Daha Fazla

Journal of Mathematical Inequalities, cilt.17, sa.1, ss.99-111, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.7153/jmi-2023-17-07
  • Dergi Adı: Journal of Mathematical Inequalities
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.99-111
  • Anahtar Kelimeler: and phrases, Abstract convexity, functional inequalities, generalized power mean, global optimization
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, the generalized power mean inequalities with a negative parameter are refined using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a refinement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exemplified by numerical calculations.