Many real-world physical problems are inherently nonlinear in nature. In most cases, obtaining their exact solutions is challenging or even impossible. Consequently, once the existence of solutions is assured, considerable attention has been devoted in developing various approximation methods to effectively tackle these nonlinear problems. In this dissertation, we construct different iterative algorithms to approximate solutions of such non-linear problems. First, we introduce λ-strict quasi-Gf-pseudocontractive mappings and propose a method for approximating the solution of the split common fixed point problem involving λ- strict quasi-Gf-pseudocontractive mapping in the setting of two Banach spaces using Gf(., .) functional. We prove that the proposed method converges strongly to a solution of the split common fixed point problem. In addition, we provide some applications of our method and provide numerical examples to demonstrate the applicability of the proposed method. Moreover, we introduce a new problem called the two-tuple split common fixed point problem in the setting of three Banach spaces. Then, we propose an inertial algorithm for approximating a solution for the two-tuple split common fixed point problem involving the class of strict quasi-ϕ-pseudocontractive mappings. As a consequence, we provide a method of approximating a solution to the split equality fixed point problem involving strict quasi-ϕ-pseudocontractive mappings in the setting of three Banach spaces. As an application of our result, we study the split equality equilibrium problem, the split equality variational inclusion problem and the split equality problem in the framework of Banach spaces. To verify our work, we give a numerical example. Furthermore, we introduce m-tuple split common fixed point problems. We present an inertial method to estimate solutions to the m-tuple split common fixed point problems for two kinds of strict quasi-Gf-pseudocontractive mappings in (m+1) Banach ix spaces. Our approach can also be used to solve the extended split equality fixed point problem. Applications to the solution of extended split equality issues are demonstrated in the framework of Banach spaces. To illustrate our conclusions, we end with a numerical example. Overall, the proposed inertial algorithm enhances convergence speed by incorporating previous iterative information and extends the analysis from Hilbert to Banach spaces. The results provide a broad theoretical framework with potential applications in signal and image reconstruction, optimization, and inverse problems.