COMPLEMENTS OF NABLA AND DELTA HARDY-COPSON TYPE INEQUALITIES AND THEIR APPLICATIONS
Miskolc Mathematical Notes, cilt.26, sa.1, ss.335-365, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 26 Sayı: 1
- Basım Tarihi: 2025
- Doi Numarası: 10.18514/mmn.2025.3825
- Dergi Adı: Miskolc Mathematical Notes
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
- Sayfa Sayıları: ss.335-365
- Anahtar Kelimeler: Copson’s inequality, Hardy’s inequality, nabla time scale calculus
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
In this paper the classical nabla and delta Hardy-Copson type inequalities, which are derived for ζ?> 1, are complemented to the new case ζ < 0. These complements have exactly the same forms as the aforementioned classical inequalities except that the exponent ζ is not greater than one but it is less than zero. The obtained inequalities are not only novel but also unify the continuous and discrete cases for which the case ζ < 0 has not been considered so far either. Moreover one of the applications of Hardy-Copson type inequalities, which is to find nonoscillation criteria for the half linear differential/dynamic/difference equations, are presented by using complementary delta Hardy-Copson type inequalities.