Some Extended Nabla and Delta Hardy-Copson Type Inequalities with Applications in Oscillation Theory

Kayar Z., Kaymakcalan B.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, cilt.48, sa.5, ss.2407-2439, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 5
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s41980-021-00651-2
  • Dergi Adı: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2407-2439
  • Anahtar Kelimeler: Time scale calculus, Hardy's inequality, Copson's inequality, Oscillation of half linear dynamic equations, INTEGRAL-INEQUALITIES, TIME SCALES, WEIGHTS
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We extend classical nabla and delta Hardy-Copson type inequalities from zeta > 1 to 0 < zeta < 1 and also use these novel inequalities to find necessary and sufficient condition for the nonoscillation of the related half linear dynamic equations. Since ordinary differential equations and difference equations are special cases of dynamic equations, our results cover these equations as well. Moreover, the obtained inequalities are not only novel but also unify the continuous and discrete cases for which the case 0 < zeta < 1 has not been considered so far.