Simpson and Newton type inequalities for convex functions via newly defined quantum integrals. (19th July 2020)

• Record Type: Journal Article
• Authors: Budak, Hüseyin; Erden, Samet; Ali, Muhammad Aamir
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 1(2021)
• Page Start: 378
• Page End: 390
• Publication Date: 2020-07-19
• Subjects: convex function -- quantum derivatives -- quantum integral inequalities -- Simpson inequality; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6742
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.