Can CVX be used for solving all the problems that can be solved by AMPL(A Mathematical Programming Language)?
Can some please suggest me some links for examples for solving max-min problems in CVX?

AMPL can be used to formulate non-convex optimization problems, as well as convex optimization problems which don’t need to follow cvx’s rule set. Solvers can be called from AMPL, although depending on the problem and the solver, not necessarily to global optimality, nor even always a local optimum.

Mark’s comment is correct, and really should be an answer. No, CVX does not solve every problem that AMPL can solve. But in fact, AMPL can’t solve every problem that CVX can solve, either! I’m afraid there is simply no substitute here for perusing the documentation, in particular the DCP ruleset and the function reference, and perusing the example library.