New general Grüss-type inequalities over σ -finite measure space with applications

Advances in Difference Equations

article

Iqbal, Sajid¹  Adil Khan, Muhammad²  Abdeljawad, Thabet³  Samraiz, Muhammad⁶  Rahman, Gauhar⁷  Nisar, Kottakkaran Sooppy⁸ 

[1] Department of Mathematics, University of Management and Technology;Department of Mathematics, University of Peshawar;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Mathematics, University of Sargodha;Department of Mathematics, Shaheed Benazir Bhutto University;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University

关键词: Grüss-type inequalities;    Kernel;    Fractional integrals;    Young’s inequality;   

DOI  :  10.1186/s13662-020-02933-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we establish some new integral inequalities involving general kernels. We obtain the related broad range of fractional integral inequalities. Also, we apply the Young inequality to find new forms of inequalities for generalized kernels. These new and motivated results generalize the results for fractional integrals such that fractional integral of a function with respect to an increasing function, Riemann–Lioville fractional integrals, Erdélyi–Kober fractional integrals, Hadamard fractional integrals, generalized factional integral integrals in addition to the corresponding k-fractional integrals.

【 授权许可】

CC BY