Jensen's inequalities for pseudo-integrals

Document Type : Research Paper


1 College of Mathematics, Changchun Normal University, Changchun 130032, Jilin, PR China

2 Singidunum University, 11000 Belgrade, Serbia


In this paper, we introduce a general
$(\oplus,\otimes)$-convex function based on semirings $([a,b],
\oplus, \otimes)$ with pseudo-addition $\oplus$ and
pseudo-multiplication $\otimes.$ The generalization of the finite
Jensen's inequality, as well as pseudo-integral with respect to
$(\oplus,\otimes)$-convex functions, is obtained.
This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and \v{S}trboja \cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], \sup, \otimes)$
with respect to nondecreasing functions and present corresponding
results for generalized fuzzy integrals.