Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

Journal of Inequalities and Applications

Juan L. G. Guirao¹  Praveen Agarwal²  Saad Ihsan Butt³  Saba Yousaf³ 

[1] Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203, Murcia, Spain;Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia;Department of Mathematics, Anand International College of Engineering, 303012, Jaipur, Rajasthan, India;Nonlinear Dynamics Research Center (NDRC), Ajman University, AE 346, Ajman, United Arab Emirates;Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan;

关键词: Harmonic convex function;    Jensen-type inequality;    Jensen–Mercer inequality;    Fractal space;    Generalized harmonic convex function;    Local fractional derivative;    Local fractional integral;    26D10;    26A51;    25D15;    26A33;   

DOI  :  10.1186/s13660-021-02735-3

来源: Springer

【 摘 要 】

In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

【 授权许可】

CC BY