Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property

Advances in Difference Equations

article

Khan, Zareen A.¹  Rashid, Saima²  Ashraf, Rehana³  Baleanu, Dumitru⁴  Chu, Yu-Ming⁵ 

[1] Department of Mathematics, College of Science, Princess Nourah bint Abdulrahman University;Department of Mathematics, Government College University;Department of Mathematics, Lahore College for Women 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: Generalized convex functions;    Hermite–Hadamard inequalty;    Čebyšev inequality;    Generalized Hölder inequality;    Power-mean inequality;    Fractal set;   

DOI  :  10.1186/s13662-020-03121-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In the paper, we extend some previous results dealing with the Hermite–Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Hölder and power-mean inequalities. As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.

【 授权许可】

CC BY