Convexity and inequalities of some generalized numerical radius functions

In this paper, we prove that each of the following functions is convex on R: f(t) = wN(AtXA1?t ? A1?tXAt), g(t) wN(AtXA1?t), and h(t) wN(AtXAt) where A > 0, X Mn N(.) a unitarily invariant norm onMn. Consequently, answer positively question concerning convexity function t w(AtXAt) proposed by in (2018). We provide some generalizations extensions wN(.) using Kwong functions. More precisely, wN(f(A)X1(A) + g(A)Xf (A)) wN(AX+XA) 2wN(X)N(A), which kind generalization Heinz inequality for generalized numerical radius norm. Finally, inequalities Schatten p-generalized partitioned 2 block matrices are established, generalize Hilbert-Schmidt given Aldalabih Kittaneh (2019).