Wirtinger integral inequalities for pseudo-integrals and pseudo-additive measure

Journal of inequalities and applications

Jing Guo¹  Xianjun Zhu² 

[1] School of Software Engineering, Jinling Institute of Technology, 211169, Nanjing, P.R. China;School of Software Engineering, Jinling Institute of Technology, 211169, Nanjing, P.R. China;Reproductive Medicine Center, Jinling Hospital, 210002, Nanjing, P.R. China;Research Center for New Technology in Intelligent Equipment, Nanjing University, 210093, Nanjing, P.R. China;

关键词: Pseudo-operations;    Pseudo-integral;    Interval-valued measure;    Pseudo-addition;    Pseudo-multiplication;    Wirtinger inequality;    03E72;    28E10;    26E50;    26D15;   

DOI  :  10.1186/s13660-021-02652-5

来源: Springer

【 摘 要 】

The main purpose of this paper is to show Wirtinger type inequalities for the pseudo-integral. We are concerned with pseudo-integrals based on the following three canonical cases: in the first case, the real semiring with pseudo-operation is generated by a strictly monotone continuous function g; in the second case, the pseudo-operations include a pseudo-multiplication and a power arithmetic addition; in the last case, ⊕-measures are interval-valued. Examples are given to illustrate these equalities.

【 授权许可】

CC BY