Symmetry, Vol. 15, Pages 1169: Some q-Symmetric Integral Inequalities Involving s-Convex Functions

Symmetry, Vol. 15, Pages 1169: Some q-Symmetric Integral Inequalities Involving s-Convex Functions

Symmetry doi: 10.3390/sym15061169

Authors: Ammara Nosheen Sana Ijaz Khuram Ali Khan Khalid Mahmood Awan Marwan Ali Albahar Mohammed Thanoon

The q-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.