Operator power means due to Lawson–Lim–Pálfia for 1<t<21<t<2

For −1≤t≤1−1≤t≤1, Lim–Pálfia defined a new family of operator power means of positive definite matrices and subsequently by Lawson–Lim their notion and most of their results extend to the setting of positive invertible operators on a Hilbert space. Each of these means except t≠0t≠0 arises as a unique positive invertible solution of a non-linear operator equation and satisfies all desirable properties of power arithmetic means of positive real numbers. The purpose of this paper is to extend the range in which operator power means due to Lawson–Lim–Pálfia are defined. We investigate some properties of operator power means for t∈(−2,2)\[−1,1]t∈(−2,2)\[−1,1].