Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings

AbstractA new class of parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings is introduced. By applying resolvent operator technique of h-maximal monotone mapping and the property of fixed point set of set-valued contractive mappings, the behavior and sensitivity analysis of the solution set of the parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings are studied. The continuity and Lipschitz continuity of the solution set with respect to the parameter are proved under suitable assumptions. Our approach and results are new and improve, unify and extend previous many known results in this field

An Ishikawa-type Iterative Algorithm for Solving A Generalized Variational Inclusion Problem Involving Difference of Monotone Operators

In this paper, we study a generalized variational inclusion problem involving difference of monotone operators in Hilbert spaces. We established equivalence between the generalized variational inclusion problem and a fixed point problem. We establish an Ishikawa type iterative algorithm for solving a generalized variational inclusion problem involving difference of monotone operators, which is more general than Mann-type iterative algorithm. An existence result as well as a convergence result are proved separately. The problem of this paper is more general than many existing problems in the literature. Several special cases of generalized variational inclusion problem involving difference of monotone operators are also mentioned

Equilibrium problems on Riemannian manifolds with applications

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on Hadamard manifolds.National Natural Science Foundation of ChinaNatural Science Foundation of Guizhou Province (China)Dirección General de Enseñanza SuperiorJunta de AndalucíaNational Science Council of Taiwa

Three-Step Iterative Algorithms for Multivalued Quasi Variational Inclusions

AbstractIn this paper, we suggest and analyze some new classes of three-step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique. New iterative algorithms include the Ishikawa, Mann, and Noor iterations for solving variational inclusions (inequalities) and optimization problems as special cases. The results obtained in this paper represent an improvement and a significant refinement of previously known results

An iterative method for generalized set-valued nonlinear mixed quasi-variational inequalities

AbstractThis paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang et al. (Comp. Math. Appl. 40 (2–3) (2000) 205–215). The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets