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...

Copyright q 2010 Yeong-Cheng Liou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present an iterative algorithm for finding a common element x * of the set of solutions of a mixed equilibrium problem and the set of a variatio...

and Applied Analysis 3 monotone and Lipschitz continuous mappings are cocoercive, and it follows that cocoercivity is an intermediate concept that lies between simple and strong monotonicity. Definition 2.3. A multivalued mapping M : X → 2 is said to be cocoercive if there exists a constant μ′′ > 0 such that 〈 u − v, x − y〉 ≥ μ′′‖u − v‖, ∀x, y ∈ X, u ∈ M x , v ∈ M(y). 2.7 Definition 2.4. Amappi...

In this paper, we introduce and consider a new system of extended general variational inclusions involving eight different operators. Using the resolvent operator techniques, we show that the new system of extended general variational inclusions is equivalent to the fixed point problem. We prove the strong convergence of some new explicit iterative parallel algorithms using resolvent methods un...

We introduce and study a new system of random nonlinear generalized variational inclusions involving random fuzzy mappings and set-valued mappings with H ·, · -monotonicity in two Hilbert spaces and develop a new algorithm which produces four random iterative sequences. We also discuss the existence of the random solutions to this new kind of system of variational inclusions and the convergence...