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http://dx.doi.org/10.5831/HMJ.2018.40.3.509

RELATIVE RECIPROCAL VARIATIONAL INEQUALITIES  

Khan, Awais Gul (Department of Mathematics, Government College University)
Noor, Muhammad Aslam (Dept of Mathematics, COMSATS Institute of Information Technology)
Pervez, Amjad (Department of Mathematics, Government College University)
Noor, Khalida Inayat (Dept of Mathematics, COMSATS Institute of Information Technology)
Publication Information
Honam Mathematical Journal / v.40, no.3, 2018 , pp. 509-519 More about this Journal
Abstract
In this paper, we introduce a new class of reciprocal convex set which is called as relative reciprocal convex set. We establish a necessary and sufficient condition for the minimum of the differentiable relative reciprocal convex function. This condition can be viewed as a new class of variational inequality which is called relative reciprocal variational inequality. Using the auxiliary principle technique we discuss the existence criteria for the solution of relative reciprocal variational inequality. Some special cases which are naturally included in our main results are also discussed.
Keywords
Reciprocal variational inequalities; Reciprocal convex functions; Auxiliary principle technique;
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