This book is devoted to related mathematics questions concerning various Banach spaces of functions reflected in separate chapters. The generalizations of Morrey spaces, Morrey-Campanato spaces, Holder spaces, the solvability of the infinite system of integral equations in Banach sequence spaces, some problems of approximation theory in variable exponent Lebesgue spaces, a nonlocal problem with nonlinearity for second order nonlinear Fredhholm integro-differential equation with degenerate kernel, etc. are considered. The results presented in this book can be useful for specialists in the fields of harmonic analysis, approximation theory, function theory, and the theory of differential equations.