Inertial Mann-Krasnoselskii algorithm with self adaptive stepsize for split variational inclusion problem and paramonotone equilibria

In this paper, we introduce a Mann-Krasnoselskii algorithm of inertial form for approximating a common solution of Spit Variational Inclusion Problem (SVIP) and Equilibrium Problem (EP) with paramonotone bifunction in real Hilbert spaces. Motivated by the self-adaptive technique, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumptions such as monotonicity and lower semicontinuity of the SVIP and EP associated mappings, we establish the strong convergence of the iterative algorithm. Some applications and numerical experiments are presented to illustrate the performance and behaviour of our method as well as comparing it with some related methods in the literature. Our results improve and generalize many existing results in this direction.