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

Advances in Difference Equations

article

Rashid, Saima¹  İşcan, İmdat²  Baleanu, Dumitru³  Chu, Yu-Ming⁴ 

[1] Department of Mathematics, Government College University;Department of Mathematics, Faculty of Arts and Sciences, Giresun University;Department of Mathematics, Faculty of Arts and Sciences, Çankaya University;Department of Mathematics, Huzhou University;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology

关键词: Convex function;    s -type convex function;    Hermite–Hadamard inequality;    Ostrowski inequality;    Higher degree polynomial s -convex;   

DOI  :  10.1186/s13662-020-02720-y

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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$\mathcal{K}$ -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.

【 授权许可】

CC BY