We give an extension of the refined Jensen’s operator inequality for n−tuples of self-adjoint operators, unital n−tuples of positive linear mappings and real valued continuous convex functions with conditions on the spectra of the operators. We also study the order among quasi-arithmetic means under similar conditions.

The class of quasi semi -convex functions and pseudo are presented in this paper by combining the with functions, respectively. Various non-trivial examples introduced to illustrate new show their relationships recently literature. Different general properties characteristics established. In addition, some optimality generalized non-linear optimization problems discussed. problems, we used, as ...