Some New Generalized Fractional Newton's Type Inequalities for Convex Functions. (2nd September 2022)

• Record Type: Journal Article
• Authors: Soontharanon, Jarunee; Ali, Muhammad Aamir; Budak, Hüseyin; Kösem, Pinar; Nonlaopon, Kamsing; Sitthiwirattham, Thanin
• Other Names: Moghaddam Behrouz Parsa Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-09-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/6261970
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we establish some new Newton's type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k -fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature.