Iterative Algorithms for General Multivalued Variational Inequalities
نویسندگان
چکیده
and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as the mildly nonlinear multivalued variational inequality and has been studied extensively. If F and A are single-valued nonlinear operators, then problem 2.1 is equivalent to finding u ∈ C such that 〈F u A u , v − u〉 ≥ 0, ∀v ∈ C, 2.5 which is known as the mildly nonlinear variational inequality, the origin of which can be traced back to Noor 15 . C If w 0 and g ≡ I, then 2.1 reduces to: find u ∈ C such that 〈F u , v − u〉 ≥ 0, ∀v ∈ C, 2.6 which is wellknown as the variational inequality, originally introduced and studied by Stampacchia 24 in 1964. It is clear from the above discussion that general multivalued variational inequality is quite general one. It has been shown that a wide class of problems arising in various discipline of mathematical and engineering sciences can be studied via the general multivalued variational inequalities 2.1 and its special cases. In the sequel, we need the following well-known lemma. Lemma 2.1. For a given z ∈ H, u ∈ C satisfies the inequality 〈u − z, v − u〉, ∀v ∈ C, 2.7
منابع مشابه
Projection Iterative Methods for Multivalued General Variational Inequalities
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...
متن کاملIterative algorithms for families of variational inequalities fixed points and equilibrium problems
متن کامل
Projection Iterative Approximations for a New Class of General Random Implicit Quasi-variational Inequalities
We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stabi...
متن کاملPii: S0898-1221(97)00049-7
-In this paper, we establish the equivalence between the generalized nonlinear variational inequalities and the generalized Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized variational inequalities. We also discuss the convergence analysis of the proposed algorithms. As a special case, we obtain various known results...
متن کاملResearch Article Wiener-Hopf Equations Technique for General Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings
We show that the general variational inequalities are equivalent to the general WienerHopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results impro...
متن کامل