纵观近年全国各省市高考数学模拟试题 ,“不动点”问题悄然兴起 .这类问题通常以“不动点”为载体 ,将函数、数列、不等式、方程、解析几何等知识有机地交汇在一起 ,因而极富思考性和挑战性 .下面笔者精选出 5道典型例题并予深刻剖析 ,旨在探索题型规律 ,揭示解题方法 .例 1　 Looking at the mathematics simulation test questions in various provinces and cities across the country in recent years, the “fixed point” problem has risen quietly. This type of problem often uses the “fixed point” as a carrier to organically integrate functions such as functions, series, inequalities, equations, and analytical geometry. Together, it is highly reflective and challenging. The following author selected five typical examples and gave them a profound analysis to explore the law of the questions and reveal the method of solving problems. Example 1