Following [1]} and Assumptions REF -REF  we have
\( \nonumber \phi _i(y_i^{k+1}) &+ \Big (\eta _i^{k} y_i + c (y_i^{k+1} - y_i^k + \delta _i^{k} ) \Big ) y_i^{k+1} \le \\ & \phi _i(y_i) + \Big (\eta _i^{k} y_i + c (y_i - y_i^k + \delta _i^{k} ) \Big ) y_i,\) 

Следуя [1] и предположениям REF-REF, у нас есть

\( \nonumber \phi _i(y_i^{k+1}) &+ \Big (\eta _i^{k} y_i + c (y_i^{k+1} - y_i^k + \delta _i^{k} ) \Big ) y_i^{k+1} \le \\ & \phi _i(y_i) + \Big (\eta _i^{k} y_i + c (y_i - y_i^k + \delta _i^{k} ) \Big ) y_i,\)