This book contains four chapters. The first one is devoted to Markov moment problem and its applications. It contains polynomial approximation results on some unbounded subsets, the link to extreme points and to Krein - Milman theorem, truncated and full moment problems, inverse problems solved starting from the moments. Solving the multidimensional Markov moment problem in terms of quadratic forms is deduced. Theorems based on an earlier result on convex distanced subsets are presented too. The second chapter studies some special functional and operatorial equations, in the real and in the complex settings. Approximation of analytic solutions is also discussed. The third chapter is devoted to convexity and approximating the perimeter of an ellipse by means of an alternate series. Minimal length surrounding curves and minimal area surrounding surfaces are also discussed. The fourth chapter recalls a variant of Newton's method for convex monotone operators. Applications in approximating of the solutions of concrete scalar and operatorial equations are deduced. The book is useful for any reader interested in these fields or in applications of analysis.