Inertial Self-Adaptive Method for Solving Fixed Point Constraint Split Common Null Point Problem (Journal of Nonlinear Modeling and Analysis, 2025)
In this manuscript, we study the split null point problem in thesettings of real Hilbert spaces using two different iterative methods. In ourfirst method, we propose a self-adaptive algorithm with an inertial techniquefor solving split common null point problem and fixed point of a finite familyof a demimetric mapping without the computation of the resolvent of a monotone operator. In our second method, we propose a self-adaptive algorithmwith a multi-step inertial technique to approximate a solution of the aforementioned problems and to accelerate the rate of convergence of our iterativemethod. The selection of the stepsize employed in our iterative algorithmsdoes not require prior knowledge of the operator norm. Lastly, we present anumerical example to show the performance of our iterative algorithms. Theresult discussed in this article extends and complements many related resultsin literature.