Nonlinear problems, including variational inequality problems and fixed point problems, are pervasive in various fields like physics, optimization, and economics. These problems often lack closed form solutions and pose significant challenges for direct analytical methods. As a result, iterative methods are widely used for approximating their solutions. In this dissertation, we study split equality problems involving common variational inequality and fixed point problems in both real Hilbert and real Banach spaces. The problems we consider are defined under weaker conditions on the associated operators and the norm, spectral radius and Lipschitz constant of these operators are not part of our conditions. We use strong convergent projection iterative methods to approximate the solutions of the problems. The methods combine inertial steps with Tseng’s extragradient method, both of which are recognized for enhancing the performance of iterative methods. First, we propose inertial-like Tseng’s extragradient and subgradient extragradient iterative algorithms for solving split equality common variational inequality and fixed point problems in real Hilbert spaces. The underlying operators associated with the variational inequality problems are quasi-monotone and uniformly continuous and those with the fixed point problems are quasi-nonexpansive operators. Under some mild conditions, we prove strong convergence of our methods to a solution of the problem and numerical examples are presented to illustrate the efficiency of the methods. Second, we introduce and study a new split equality problem with common variational inequality and fixed point problems associated with finite families of operators in the setting of real Hilbert spaces. We propose an inertial Tseng’s extragradient iterative method with viscosity technique and prove its strong convergence to a solution under some suitable conditions. We also present some numerical experiments to illustrate and show the efficiency of the proposed method. Thirdly, we study a split equality problem involving common Minty variational inequality and fixed point problems in real reflexive Banach spaces. Unlike the existing results on Minty variational inequality problems, we consider the operators to be both quasi-monotone and uniformly continuous. Under some suitable conditions, we establish a strong convergence of the proposed method to a solution of the problem. Finally, we present some numerical experiments to illustrate and show the efficiency of the method. These findings provide a scalable and theoretically robust framework for solving complex problems such as convex and nonconvex optimization problems, game-theory, engineering and economics.