In this paper we show that if Ai; Bi;Xi are Hilbert space operators such that Xi is compact i = 1; 2; : : : ; n and f , 1 are non-negative continuous functions on [0;1) with f (t)1(t) = t for all t 2 [0;1), also h is non-negative increasing operator convex function on [0;1), then h 0BBBB@ sj 0BBBB@ Xn i=1 !iA iX iBi 1CCCCA 1CCCCA sj 0BBBB@ Xn i=1 !ih(A i f (jX i j)2Ai) Xn i=1 !ih(B i 1(jXij)2Bi) 1CCCCA for j = 1; 2; : : : and Pni =1 !i = 1. Also, applications of some inequalities are given.