Monotonicity Preserving Rational Quadratic Fractal Interpolation Functions

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="504825.fig.002a" src="https://static.hindawi.com/articles/ana/volume-2014/504825/figures/504825.fig.002a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Rational FIF <svg height="11.3125" id="M158" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.9375 11.3125" width="12.9375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="504825.fig.002b" src="https://static.hindawi.com/articles/ana/volume-2014/504825/figures/504825.fig.002b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="20.725" id="M159" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 99.512497 20.725" width="99.512497" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="504825.fig.002c" src="https://static.hindawi.com/articles/ana/volume-2014/504825/figures/504825.fig.002c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b><svg height="20.875" id="M160" style="vertical-align:-4.15506pt" version="1.1" viewbox="0 0 99.775002 20.875" width="99.775002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.875,11.875)"><path d="M658 624q-60 -84 -176 -84q-59 0 -166 25q-89 21 -140 21q-80 0 -159 -54l-17 25q75 84 184 84q57 0 158 -26q100 -20 151 -20q87 0 148 54z" id="xF5C12"></path></g><g transform="matrix(.017,-0,0,-.017,59.312,10.962)"><path d="M470 619q-46 -79 -133 -79q-39 0 -115 22q-59 16 -92 16q-57 0 -111 -46l-19 23q56 78 138 78q43 0 110 -21q62 -17 100 -17q60 0 103 46z" id="xF5C11"></path></g><g transform="matrix(.017,-0,0,-.017,54.625,15.637)"><path d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19
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</svg></td></tr></table></td></tr></table>

<table>Rational FIF and its integrals.</table>

Advances in Numerical Analysis

fig2

Figure 2

Figure 2: Monotonicity Preserving Rational Quadratic Fractal Interpolation Functions 