Norm inequalities for Heinz and Heron means via contractive maps

In this paper, using the contractive maps, we present some new interpolations between the Heinz and Heron operator means for unitarily invariant norms. Let A,X,B is an element of B(H) and A,B be two positive definite operators. and let 1/2 <= beta <= 1, alpha is an element of [1/2, infinity). If 1/4 <= nu <= mu <= 1/2 and mu+nu/2 <= r <= 1 - mu+nu/2, or if 1/2 <= mu <= nu <= 3/4 and 1 - mu+nu/2 <= r <= mu+nu/2, then parallel to vertical bar H-r(A,X,B)parallel to vertical bar <= parallel to vertical bar (1-beta)H-mu(A,X,B) + beta H-nu(A,X,B)parallel to vertical bar <= parallel to vertical bar F-alpha(A,X,B)parallel to vertical bar . We also consider some Heinz-type inequalities that involve differences and sums of operators. We give new forms and reverse inequalities of the presented inequalities by Singh et al.