Generation of new fractional inequalities via n polynomials s-type convexity with applications

• Main Authors: Saima Rashid, İmdat İşcan, Dumitru Baleanu, Yu-Ming Chu
• Format: Article
• Language: English
• Published: SpringerOpen 2020-06-01
• Series: Advances in Difference Equations
• Subjects: Convex function; s-type convex function; Hermite–Hadamard inequality; Ostrowski inequality; Higher degree polynomial s-convex
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02720-y

Abstract The celebrated Hermite–Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite–Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing K $\mathcal{K}$ -fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning.