A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions. (23rd October 2021)

• Record Type: Journal Article
• Authors: Ali, Muhammad Aamir; Budak, Hüseyin; Zhang, Zhiyue
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 4(2022)
• Page Start: 1845
• Page End: 1863
• Publication Date: 2021-10-23
• Subjects: convex functions -- Newton's inequalities -- quantum calculus -- Simpson's inequalities; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7889
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.