SUMMARY
One solves Markov moment and Mazur-Orlicz problems in concrete spaces of functions and respectively operators. One uses earlier results, as well as recent theorems on the subject. One characterizes the existence of a solution, or one gives sufficient conditions for it does exist. Sometimes the uniqueness of the solution of some moment problems follows too. Spaces of continuous, of integrable and respectively analytic functions are considered as domain space of the solution. Usually, an order complete Banach lattice of self-adjoint operators (the bicommutant) is the target-space. Results on the abstract Markov moment problem, the abstract version of Mazur-Orlicz theorem and appropriate knowledge in functional analysis are applied. Basic elements of measure theory and Cauchy inequalities are used as well.