The other term has already spent the budget

Let $f:\mathbb{R}\to \mathbb{R}$ be such that sup(x≠y) |f(x) − f(y)|/|x − y| = L, where $1<L<\infty$. Let $h:\mathbb{R}\to \mathbb{R}$ be a differentiable function satisfying |h′(x)| ≤ 3/4 for all $x\in \mathbb{R}$. For $\alpha >0$, define $g(x)=\alpha f(x)+h(x)$ for $x\in \mathbb{R}$. Consider the sequence {$x_k$}(k≥0) defined by $x_{(}k+1)=g(x_k),k=0,1,\dots$, where $x_0\in \mathbb{R}$. The sequence {$x_k$}(k≥0) converges to the solution of the equation x = g(x) if