Table 1 The solutions obtained by the new modified Ishikawa iteration method for different values of λ and γ

x = 0.2

$\begin{array}{l}{y}_1=1.2\\ y_2=1.1\\ y_3=1.15\\ y_4=1.125\\ y_5=1.1375\\ y_6=1.13125\\ y_7=1.134375\\ y_8=1.1328125\\ y_9=1.13359375\\ y_{10}=1.133203125\\ y_{11}=1.13398437\end{array}$

$\begin{array}{l}{y}_1=1.2\\ y_2=1.05\\ y_3=1.125\\ y_4=1.06875\\ y_5=1.096875\\ y_6=1.07578125\\ y_7=1.086328125\\ y_8=1.078417968\\ y_9=1.082373046\\ y_{10}=1.079406738\\ y_{11}=1.080889892\end{array}$

$\begin{array}{l}{y}_1=1.2\\ y_2=1.1\\ y_3=1.125\\ y_4=1.1125\\ y_5=1.115625\\ y_6=1.1140625\\ y_7=1.114453125\\ y_8=1.114257812\\ y_9=1.11430664\\ y_{10}=1.114282226\\ y_{11}=1.11428833\end{array}$

$\begin{array}{l}{y}_1=1.2\\ y_2=1.05\\ y_3=1.0875\\ y_4=1.059375\\ y_5=1.06640625\\ y_6=1.06113281\\ y_7=1.062451171\\ y_8=1.061462402\\ y_9=1.061709594\\ y_{10}=1.0615242\\ y_{11}=1.061570548\end{array}$

x = 0.4

$\begin{array}{l}{y}_1=1.4\\ y_2=1.2\\ y_3=1.3\\ y_4=1.25\\ y_5=1.275\\ y_6=1.2625\\ y_7=1.26875\\ y_8=1.265625\\ y_9=1.2671875\\ y_{10}=1.26640625\\ y_{11}=1.266796874\end{array}$

$\begin{array}{l}{y}_1=1.4\\ y_2=1.1\\ y_3=1.25\\ y_4=1.1375\\ y_5=1.19375\\ y_6=1.1515625\\ y_7=1.17265625\\ y_8=1.156835937\\ y_9=1.164746093\\ y_{10}=1.158813476\\ y_{11}=1.161779784\end{array}$

$\begin{array}{l}{y}_1=1.4\\ y_2=1.2\\ y_3=1.25\\ y_4=1.225\\ y_5=1.23125\\ y_6=1.228125\\ y_7=1.22890625\\ y_8=1.228515624\\ y_9=1.228613281\\ y_{10}=1.228564452\\ y_{11}=1.22857666\end{array}$

$\begin{array}{l}{y}_1=1.4\\ y_2=1.1\\ y_3=1.175\\ y_4=1.11875\\ y_5=1.1328125\\ y_6=1.122265624\\ y_7=1.124902343\\ y_8=1.122924804\\ y_9=1.123419189\\ y_{10}=1.1230484\\ y_{11}=1.123141097\end{array}$

x = 0.5

$\begin{array}{l}{y}_1=1.5\\ y_2=1.25\\ y_3=1.375\\ y_4=1.3125\\ y_5=1.34375\\ y_6=1.328125\\ y_7=1.3359375\\ y_8=1.33203125\\ y_9=1.333984375\\ y_{10}=1.333007812\\ y_{11}=1.333496093\end{array}$

$\begin{array}{l}{y}_1=1.5\\ y_2=1.125\\ y_3=1.3125\\ y_4=1.171875\\ y_5=1.2421875\\ y_6=1.189453125\\ y_7=1.215820312\\ y_8=1.196044921\\ y_9=1.205932617\\ y_{10}=1.198516845\\ y_{11}=1.202224731\end{array}$

$\begin{array}{l}{y}_1=1.5\\ y_2=1.25\\ y_3=1.3125\\ y_4=1.28125\\ y_5=1.2890625\\ y_6=1.28515625\\ y_7=1.286132812\\ y_8=1.285644531\\ y_9=1.285766601\\ y_{10}=1.285705566\\ y_{11}=1.285720825\end{array}$

$\begin{array}{l}{y}_1=1.5\\ y_2=1.125\\ y_3=1.21875\\ y_4=1.1484375\\ y_5=1.166015625\\ y_6=1.152832031\\ y_7=1.156127929\\ y_8=1.153656005\\ y_9=1.154273986\\ y_{10}=1.1538105\\ y_{11}=1.153926372\end{array}$