Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m) -preinvex functions

By Tingsong Du, Jiagen Liao, Yujiao Li. 2016

128 citations recorded by the source corpus.

The authors introduce the concepts of m-invex set, generalized (s,m)-preinvex function, and explicitly (s,m)-preinvex function, provide some properties for the newly introduced functions, and establish new Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first derivative is generalized (s,m)-preinvex function. By taking different values of the parameters, Hadamardtype and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results. c ©2016 All rights reserved.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/d8d6e66e41f1e1e818fecd7c860d8e28fd68817a