Abstract
In this paper, we study a new kind of existence of solution for set valued exponential type mixed vector variational-like inequality problem in Euclidean space and proposed αg-relaxed exponentially (γ,η)-monotone mapping. Moreover, we established an example in order to illustrate the main problem. We proved the existence results by KKM-technique with αg-relaxed exponentially (γ,η)-monotone mapping. Further, we give some consequences of the main result. The results presented in this paper unifies and extends some known results in this area.
Highlights
The theory of vector variational inequality has been introduced by Giannessi [7] in 1980 for finite dimensional space
We study a new kind of existence of solution for set valued exponential type mixed vector variational-like inequality problem in Euclidean space and proposed αg-relaxed exponentially (γ, η)-monotone mapping
Wu and Huang [16] defined the concepts of relaxed η − α pseudomonotone mappings to study vector variational-like inequality problem in Banach spaces
Summary
The theory of vector variational inequality has been introduced by Giannessi [7] in 1980 for finite dimensional space.
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