On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations

<table>Behaviour of the number of iterations for convergence with the starting point <svg height="11.075" id="M161" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.8125 11.075" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.075)">
<g transform="translate(72,-63.14)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
</g>
</g>
</svg> of the member <svg height="13.55" id="M162" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 47.775002 13.55" width="47.775002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
<tspan style="font-size: 12.50px; " x="10.440005" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.480394" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.731894" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.857643" y="0">2</tspan>
</text>
</g>
</g>
</svg> of the 16th FK  family for the function <svg height="14.5625" id="M163" style="vertical-align:-3.20526pt" version="1.1" viewbox="0 0 14.8875 14.5625" width="14.8875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.5625)">
<g transform="translate(72,-60.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.01,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">7</tspan>
</text>
</g>
</g>
</svg>.</table>

International Journal of Mathematics and Mathematical Sciences

fig3

Figure 3

Figure 3: On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations 