I am working on optimization of an objective function which is a ratio of two linear functions given as mx + b/-mx+c. Can somebody comment about convexity of this function and/or give me some reference?
You might consider consulting Stephen Boyd's convex optimization book. Section 3.4 (example 3.32) is what you are interested in. Your example is called a linear fractional function and is indeed quasiconvex and quasiconcave if you restrict the domain of the denominator to be either greater or less than 0. Quasiconvex optimization problems can be solved using a method like bisection which involves solving a series of feasibility problems