In this paper, we introduce a new generalized mixed exponential type vector variational-like inequality problems (GMEVVLIP) and \(\alpha \)-relaxed exponentially \((p,\eta )\)-monotone mapping. We prove the existence results of (GMEVVLIP) by utilizing the KKM technique and Nadlar’s results with \(\alpha \)-relaxed exponentially \((p,\eta )\)-monotone mapping in Euclidian spaces. The present work extends some corresponding results of (GMEVVLIP) .
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