Metrics That Suit for Dichotomy, Well Conditioning and Object Oriented Design on Measure Chains

The paper deals with Dichotomy, well conditioning of two-point boundary value problems on time scale dynamical systems using a suitable norm on $R^{n}$. The results presented in this paper on Dichotomy and well conditions of two-point boundary value problems unify both continuous and discrete systems and generalizes these results on time scale dynamical systems. We also present empirical validation of a set of theoretical-grounded metrics on object-oriented design. Fixed point theory on metric spaces is used as a tool to obtain the required object in object oriented designs and in designing flows.