About principle of compression operators and succesive approximantion method and some of their applications

In this thesis, principle of compression operators was studied, examined and learned for linear and nonlinear A:X→X operators which transforms X Banach space to X Banach space itself. Solution method for equations those have compression operators in Banach space with successive approximation method, was studied and examined. In different examples, finding approximate solutions of algebraic linear equations, integral equations and ordinary differential equations with successive approximation method was shown Keywords: principle of compression operators, successive approximation method, operator equations, integral eqvations, differential equations.