In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

<p style='text-indent:20px;'>The purpose of this paper is to introduce a new inertial iterative method for solving split variational inclusion problems in real Hilbert spaces. We prove that the generated sequence converges weakly solution considered problem under some mild conditions. The major contributions our results are: (ⅰ) increase rate convergence through extrapolation step, (ⅱ) re...

Tseng's forward-backward-forward splitting method for finding zeros of the sum Lipschitz continuous monotone and maximal operators is known to converge weakly in infinite dimensional Hilbert spaces. The inertial viscosity approximation techniques are widely used accelerate iterative algorithms obtain strong convergence, respectively. In this paper, we propose two fast, strongly convergent modif...

We study maximal monotone inclusions from the perspective of (convex) gap functions. We propose a very natural gap function and will demonstrate how this function arises from the Fitzpatrick function — a convex function used effectively to represent maximal monotone operators. • This approach allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. – We...