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We show the following result: Let $A,B\in \mathbb{B}\left( \mathcal{H}\right)$ be two strictly positive operators such that $A\le B$ and$m{{\mathbf{1}}_{\mathcal{H}}}\le B\le M{{\mathbf{1}}_{\mathcal{H}}}$ for somescalars $0<m<M$. Then \[{{B}^{p}}\le \exp \left(\frac{M{{\mathbf{1}}_{\mathcal{H}}}-B}{M-m}\ln{{m}^{p}}+\frac{B-m{{\mathbf{1}}_{\mathcal{H}}}}{M-m}\ln {{M}^{p}} \right)\leK\left( m,M,p,q \right){{A}^{q}}\quad\text{ for }p\le 0,-1\le q\le 0\] where$K\left( m,M,p,q \right)$ is the generalized Kantorovich constant with twoparameters. In addition, we obtain Kantorovich type inequalities for thechaotic order.

New Inequalities of the Kantorovich Type With Two Negative Parameters