TY - JOUR AU - Khalid, Sadia AU - Pečarić, Josip PY - 2020 DA - 2020/12/21 TI - Refinements of some Hardy–Littlewood–Pólya type inequalities via Green’s functions and Fink’s identity and related results JO - Journal of Inequalities and Applications SP - 260 VL - 2020 IS - 1 AB - In this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex functions. We also present refinements of some Hardy–Littlewood–Pólya type inequalities and give an application to the Shannon entropy. Furthermore, we use the Čebyšev functional and Grüss type inequalities and present the bounds for the remainder in the obtained identities. Finally, we use the obtained identities together with Hölder’s inequality for integrals and present Ostrowski type inequalities. SN - 1029-242X UR - https://doi.org/10.1186/s13660-020-02498-3 DO - 10.1186/s13660-020-02498-3 ID - Khalid2020 ER -