Abstract
In this study, we introduce and study a generalized complementarity problem involving XOR operation and three classes of generalized variational inequalities involving XOR operation. Under certain appropriate conditions, we establish equivalence between them. An iterative algorithm is defined for solving one of the three generalized variational inequalities involving XOR operation. Finally, an existence and convergence result is proved, supported by an example.
Highlights
It is well known that the many unrelated free boundary value problems related to mathematical and engineering sciences can be solved by using the techniques of variational inequalities
Complementarity theory is an important area of operations research and application oriented. e linear as well as nonlinear programs can be distinguished by a family of complementarity problems. e complementarity theory have been elongated for the purpose of studying several classes of problems occurring in fluid flow through porous media, economics, financial mathematics, machine learning, optimization, and transportation equilibrium, for example, [1,2,3,4,5]
Some problems related to variational inclusions involving XOR operation were studied by [13,14,15,16]
Summary
It is well known that the many unrelated free boundary value problems related to mathematical and engineering sciences can be solved by using the techniques of variational inequalities. Some problems related to variational inclusions involving XOR operation were studied by [13,14,15,16]. An existence and convergence result is proved for one of the three types of generalized variational inequalities involving XOR operation. We consider the following generalized complementarity problem involving XOR operation. We denote by SC⊕ the solution set of generalized complementarity problem involving XOR operation (9). We remark that for suitable choices of operators involved in the formulation of (9), a number of known complementarity problems can be obtained for example, [17, 22,23,24]. We study the following three types of generalized variational inequalities involving XOR operation. Many known variational inequality problems can be obtained from problems (12)–(14), for example, [25,26,27,28,29] and the references therein
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