We introduce a new system of general variational inequalities in Banach spaces. The equivalence between this system of variational inequalities and fixed point problems concerning the nonexpansive mapping is established. By using this equivalent formulation, we introduce an iterative scheme for finding a solution of the system of variational inequalities in Banach spaces. Our main result extend...

1 Convex Relaxation Techniques for Segmentation, Stereo and Multiview Reconstruction 2 1.1 Variational Methods, Partial Differential Equations and Convexity 2 1.2 Image Segmentation and Minimal Partitions 4 1.2.1 Classical Variational Approaches 4 1.2.2 A General Variational Formulation 5 1.2.3 Convex Representation 6 1.2.4 Convex Relaxation 8 1.2.5 Experimental Segmentation Results 9 1.3 Stere...

In this paper, we consider extended general variational inequalities involving nonlinear operators. Using projection operator technique, we show that extended general variational inequality is equivalent to a fixed point problem. Using this alternative equivalent formulation, we propose and analyze some new algorithms for solving extended general variational inequalities and its variant forms. ...

In this paper, we introduce a new class of variational inequalities involving two operators. Using the projection technique, we establish the equivalence between the multivalued general variational inequalities and the fixed point problems. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the multivalued general variational inequalities. We also d...