Some new bounds оf Gauss – Jacobi аnd Hermite – Hadamard type integral inequalities

• Дата: 2021
• Автори: Kashuri, A., Ramosaçaj, M., Liko, R., Kashuri, Artion, Ramosaçaj, Miftar, Liko, Rozana
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2021
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/603
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 In this paper, authors discover two interesting identities regarding Gauss–Jacobi and Hermite–Hadamard type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss–Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite–Hadamard type integral inequalities via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal are provided as well. These results give us the generalizations, refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.