Equation goes outside the boundary with eqnarray environment!
You have to break the too-long equation manually. Here's a way to do so it seems natural, using some spacing adjustment via \phantom
:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\alpha + M(d(fx_n,fz_n)) &\leq \alpha + \alpha(fx_n,fz_m) M(d(fx_n,fz_k)) \\
&\leq M(M_{f,h}(fx_n,fz)) \\
&= M(x,y) \max \bigl\{ d(fx_n,fz),d(fx_n,fx_n), \\
&\phantom{{}={} M(x,y) \max \bigl\{}d(fz,fz),\tfrac{d(fx_n,fz)+d(fz_b,fx_n)}{h} \bigr\}
\end{align*}
\end{document}
Please avoiding using eqnarray
.
Another align*
-based solution. It differs from @Werner's solution in the way the final row's indentation is achieved and in the treatment of the fractional expression in the final row.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\alpha+M(d(fx_n,fz_n))
&\leq\alpha+\alpha(fx_n,fz_m)M(d(fx_n,fz_k))\\
&\leq M(M_{f,h}(fx_n,fz))\\
&= M(x,y)\max\bigl\{ d(fx_n,fz),d(fx_n,fx_n),\\
&\qquad\qquad d(fz,fz),\tfrac{1}{h}\bigl[d(fx_n,fz)+d(fz_b,fx_n)\bigr] \bigr\}
\end{align*}
\end{document}
I'll add three other variants:
\documentclass{article}
\usepackage[showframe]{geometry}%
\usepackage{mathtools, nccmath}
\begin{document}
\begin{align*}
\alpha+M(d(fx_n,fz_n))
& \leq\alpha+α(fx_n,fz_m)M(d(fx_n,fz_k)) \\
& \leq M(M_{f,h}(fx_n,fz)) \\
& =\!\begin{multlined}[t] M(x,y)\max\bigl\{ d(fx_n,fz),d(fx_n,fx_n), d(fz,fz), \\[0.5ex]
\mfrac{1}{h}\bigl[d(fx_n,fz)+d(fz_b,fx_n)\bigr] \bigr\}
\end{multlined}
\end{align*}
\begin{align*}
\alpha+M(d(fx_n,fz_n))
&\leq\alpha+α(fx_n,fz_m)M(d(fx_n,fz_k))\\
&\leq M(M_{f,h}(fx_n,fz))\\
& =\!\begin{aligned}[t] M(x,y)\max\bigl\{ d(fx_n,fz),d(fx_n,fx_n), d(fz,fz) & , \\
\mfrac{1}{h}\bigl[d(fx_n,fz)+d(fz_b,fx_n) & \bigr] \bigr\}
\end{aligned}
\end{align*}
\begin{align*}
\alpha+M(d(fx_n,fz_n))
& \leq\alpha+α(fx_n,fz_m)M(d(fx_n,fz_k)) \\
& \leq M(M_{f,h}(fx_n,fz)) \\
& =\! M(x,y)\max \!\begin{Bmatrix*}[r]d(fx_n,fz),d(fx_n,fx_n), d(fz,fz), \\[0.5ex]
\mfrac{1}{h}\bigl[d(fx_n,fz)+d(fz_b,fx_n)\bigr]
\end{Bmatrix*}
\end{align*}
\end{document}