In this paper, we prove the existence theorem for a mapping defined by T = T1 + T2 when T1 is a μ1-Lipschitz continuous and γ-strongly monotone mapping, T2 is a μ2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17]. Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10...

In this paper, we suggest and analyze both explicit and implicit iterative schemes for two strongly positive operators and a nonexpansive mapping S on a Hilbert space. We also study explicit and implicit versions of iterative schemes for an inverse-strongly monotone mapping T and S by an extragradient-like approximation method. The viscosity approximation methods are employed to establish stron...

The main aim of this research is to introduce and investigate an inertial Tseng iterative method approximate a common solution for the variational inequality problem γ-inverse strongly monotone mapping inclusion in real Hilbert spaces. We establish strong convergence theorem our suggested proposed problems under some certain mild conditions. Furthermore, we deduce consequence from result. Final...

In this paper, we introduce an iterative scheme by viscosity approximation method for obtaining a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. We obtain a strong convergence which improves and extends S. Tak...

We introduce a new general iterative scheme for finding a common element of the set of solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed points of a nonexpansive mapping in a Hilbert space and then establish strong convergence of the sequence generated by the proposed iterative scheme to a common element of the above two sets under suitabl...

Let C be a closed convex subset of a real Hilbert space H. Let T be a supper hybrid mapping of C into H, let A be an inverse strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C. In this paper, we introduce two iterative sequences by hybrid methods of finding a point of F (T )∩ (A+B)−10, where F (T ) is the set of fixed p...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Full list of author information is available at the end of the article Abstract Without the strong monotonicity assumption of the mapping, we provide a regularization method for general variational inequality problem, when its solution set is related to a solution se...

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the a...