\displaystyle\begin{gathered} 0 \leqslant {v_\lambda }(x) - v(x) = \int_{{\Sigma _\lambda }} {\left( {\frac{1}{{{{\left| {x - y} \right|}^{n - \alpha }}}} - \frac{1}{{{{\left| {{x^\lambda } - y} \right|}^{n - \alpha }}}}} \right)\left( {{v_\lambda }{{(y)}^\tau } - v{{(y)}^\tau }} \right)dy} \hfill \\ \quad\leqslant \int_{\Sigma _\lambda ^ - } {\left( {\frac{1}{{{{\left| {x - y} \right|}^{n - \alpha }}}} - \frac{1}{{{{\left| {{x^\lambda } - y} \right|}^{n - \alpha }}}}} \right)\left( {{v_\lambda }{{(y)}^\tau } - v{{(y)}^\tau }} \right)dy} \hfill \\ \quad= \int_{\Sigma _\lambda ^ - } {\left( {\frac{1}{{{{\left| {x - y} \right|}^{n - \alpha }}}} - \frac{1}{{{{\left| {{x^\lambda } - y} \right|}^{n - \alpha }}}}} \right){v_\lambda }(y)\left( {{v_\lambda }{{(y)}^{\tau - 1}} - v{{(y)}^{\tau - 1}}\frac{{v(y)}}{{{v_\lambda }(y)}}} \right)dy} \hfill \\ \quad\leqslant \int_{\Sigma _\lambda ^ - } {\left( {\frac{1}{{{{\left| {x - y} \right|}^{n - \alpha }}}} - \frac{1}{{{{\left| {{x^\lambda } - y} \right|}^{n - \alpha }}}}} \right){v_\lambda }(y)\left( {{v_\lambda }{{(y)}^{\tau - 1}} - v{{(y)}^{\tau - 1}}} \right)dy} \hfill \\ \quad\leqslant \int_{\Sigma _\lambda ^ - } {\left( {\frac{1}{{{{\left| {x - y} \right|}^{n - \alpha }}}}} \right){v_\lambda }(y)\left( {{v_\lambda }{{(y)}^{\tau - 1}} - v{{(y)}^{\tau - 1}}} \right)dy} . \hfill \\ \end{gathered}