On Stability of Solutions to Systems of Convex Inequalities

For systems of relations $\varphi_t(x)\le p_t,\; t\in T$, $Ax=y$, where $T$ is an arbitrary set, $\varphi_t$ is a convex l.s.c. function on a Banach space $X$ for every $t$ and $A$ is a linear bounded operator from $X$ into another Banach space $Y$, we discuss the following three problems:
(a) stability of solutions with respect to variations of the right hand side;
(b) effect of linear perturbations of functions $\varphi_t$ and mapping $A$;
(c) distance to infeasibility (the minimal norm of linear perturbations that make the system infeasible.)