Yasir Arfat

This paper introduces a novel parallel hybrid algorithm, based on an accelerated shrinking projection method, for solving the Split Monotone Variational Inclusion problems with multiple output sets in Hilbert spaces. Under an appropriate set of conditions, we establish the strong convergence of the proposed algorithm. Its practical viability is further demonstrated through a numerical experiment. The results obtained herein generalize and improve upon several existing findings in the literature.

Within the context of Hilbert spaces, we demonstrate the robust convergence of a hybrid steepest-descent approximant towards a solution for a convex minimization problem. This problem is situated within the space of solutions for equilibrium problems and the fixed point set of a finite family of η-demimetric operators. Additionally, we present numerical results that shed light on the effectiveness of the proposed approximants, offering insights into potential applications.

In this paper, we consider an accelerated shrinking projection based parallel hybrid algorithm to study the split null point problem (SNPP) associated with the maximal monotone operators in Hilbert spaces. The analysis of the proposed algorithm provides strong convergence results under suitable set of control conditions as well as viability with the help of a numerical experiment. The results presented in this paper improve various existing results in the current literature.