STRONG CONVERGENCE THEOREM FOR UNIFORMLY L-LIPSCHITZIAN MAPPING OF GREGUS TYPE IN BANACH SPACES

In this paper, we introduced a new mapping called Uniformly L-Lipschitzian mapping of Gregus type, and used the Mann iterative scheme to approximate the fixed point. A Strong convergence result for the sequence generated by the scheme is shown in real Banach space. Our result generalized and unifybmany recent results in this area of research. In addition, using Java(jdk1.8.0_101), we give a numericalbexample to support our claim.

Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints

In this paper, we introduce an iterative scheme with inertial effect using Mann iterative scheme and gradient-projection for solving the bilevel variational inequality problem over the intersection of the set of common fixed points of a finite number of nonexpansive mappings and the set of solution points of the constrained optimization problem. Under some mild conditions we obtain strong convergence of the proposed algorithm. Two examples of the proposed bilevel variational inequality problem are also shown through numerical results.

Krasnoselskii-Mann method for multi-valued non-self mappings in CAT(0) spaces

We define Mann iterative scheme in CAT(0) spaces and obtain 4-convergence and strong convergence of the iterative scheme to a fixed point of multi-valued nonexpansive non-self mappings. We also obtain strong convergence of the scheme to a fixed point of multi-valued quasi-nonexpansive non-self mappings under appropriate conditions. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.