Dr Marjan Praljak from the University of Zagreb, Croatia presented his research paper on positivity of weighted averages of higher order
convex function and informed the conference about the results obtained by finding suitable representations of polynomial part and the error term in appropriate form.
Hanson [1] introduced the generalized version of
convex function namely invex function.
Let g : C [right arrow] R be a strictly real-valued
convex function.
Since [h.sup.b.sub.i] is a
convex function, it holds that
(iii) a
convex function if satisfying (i) and (ii).
A function f : I [subset not equal to] R [right arrow] R is said to be
convex function if
Indeed, take a [v.sub.n] [member of] U, supported on [X.sub.n], so that [[parallel][x.sub.n] + [v.sub.n][parallel].sub.n] > [[parallel][x.sub.n][parallel].sub.n] and consider the
convex function [h.sub.n](t) = [??][[parallel][x.sub.n] [+ or -] t[v.sub.n][parallel].sub.n].
If [mathematical expression not reproducible] then f([u.sub.1]) is a
convex function of [u.sub.1] where [mathematical expression not reproducible] is t- distribution with [n.sub.1] - 1 degrees of freedom.
Moreover, if the fuzzy Hessian matrix [[??].sub.m] is positive semidefinite then, by Theorem 17, the objective function will also be a fuzzy-valued
convex function with respect to [less than or equal to]w.