For a maximal monotone operator T in a Banach space an iterative solution of 0 ∈ Tx has been found through weak and strong convergence of resolvents of these operators. Identity mapping in the definition of resolvents has been replaced by the duality mapping. Solution after finite steps has also been established.

Robot localization and mapping algorithms commonly represent the world as a static map. In reality, human environments consist of many movable objects like doors, chairs and tables. Recognizing that such environment often have a large number of instances of a small number of types of objects, we propose an alternative approach, Model-Instance Object Mapping that reasons about the models of obje...

In this paper, we present an iterative method for fixed point problems and variational inequality problems. Our method is based on the so-called extragradient method and viscosity approximation method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for monotone mapping.

We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.

and Applied Analysis 3 literature. For some works related to the equilibrium problem, fixed point problems, and the variational inequality problem, please see 1–57 and the references therein. However, we note that all constructed algorithms in 7, 9–13, 16, 57 do not work to find the minimum-norm solution of the corresponding fixed point problems and the equilibrium problems. Very recently, Yao ...

For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent [Formula: see text] holds shy set in measure-theoretic sense. This exhibits admit no observable chaos, notion of which was formulated by L.S. Young. We further such phenomenon chaos is robust under text]-perturbation systems.