Using extension results for linear operators with two constraints in solving Markov moment problems is a modern technique. Approximation type results are also useful in our days, as well as geometric aspects of functional and classical analysis. The present book contains five chapters related to the above mentioned topics: new results on Markov moment problem, minimum norm elements, Newton's method for convex monotone operators, equilibrium values and constant rates in interconversion processes, constructive methods in the implicit function principle. The book is written for anyone which is interested in these fields.