On explicit relations for values of Kaneko-Tsumura's $\lambda$ function

Recently, Kaneko and Tsumura introduced multiple $\tilde{T}$-values, another kind of poly-Euler numbers and the related Arakawa-Kaneko type zeta function. It is shown that each of them satisfies similar formulas to those of multiple zeta values, poly-Bernoulli numbers and the related Arakawa-Kaneko type zeta function. In this paper, we show some explicit relations for values of Kaneko-Tsumura $\lambda$ function at positive integers, including the duality type relation.