A method involving tri-inertial-type for solving split problems with multiple output sets

Abstract 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.