In this paper, we introduce two new classes of mappings known as $\lambda$-enriched strictly pseudocontractive mappings and ${\Phi }_T$-enriched Lipshitizian mappings in the setup of a real Banach space. In addition, a new modified mixed-type Ishikawa iteration scheme was constructed, and it was proved that our iteration method converges strongly to the common fixed points of finite families of the above mappings in the framework of a real uniformly convex Banach space. Moreover, we provided a non-trivial example to support our main result. Our results extend and generalize several results existing in the literature.

In this paper, an iterative scheme for finding common solutions of the set of fixed points for a pair of asymptotically quasi-nonexpansive mapping and the set of minimizers for the minimization problem is constructed. Using the idea of the jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on the space or the operator. Our results improve, extend and generalize many important results in the literature.

This paper studies a strongly convergent of a modified tri-inertial viscosity self-adaptive technique for common solution to the split generalized equilibrium problem together with the split common null point problem with multiple output sets. In our convergent analysis, no assumption was made of the sum condition on the iteration parameters, which is not the case for several results that involve strongly convergent algorithm with inertial extrapolation step proposed for split generalized equilibrium problem and split common null point problem with multiple output sets. The method uses variable step-sizes that are modified at each iteration and dependent on prior iterations. This method has the advantage of not requiring a prior knowledge of the Lipschitz constant and the linesearch process. A series of numerical experiments are performed to validate the efficacy and superiority of the presented iterative technique over the existing methods in this direction. The experiment serves to affirm the effectiveness of the proposed algorithm in split generalized equilibrium problem and split common null point problem with multiple output sets in real Hilbert spaces.

This paper advises and examines a strongly convergent relaxed bi-inertial Tseng’s extragradient method for approximating solutions to split variational inequality problems with multiple output sets. In our convergence results, we made no assumption about the sum condition on the iteration parameters, which differs from several existing results in this direction. The method employs variable step sizes that are modified at each iteration and depend on the results of previous iterations. This method has the advantage of requiring no prior knowledge of both the Lipschitz constant and the line search process. A series of numerical experiments was conducted to validate the efficacy and superiority of the presented iterative technique over existing methods in this area. The experiment confirms the effectiveness of the proposed algorithm for split variational inequality problems with multiple output sets in real Hilbert spaces.