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This article explores a new type of nonlinear complementarity problem, namely the horizontal tensor complementarity problem (HTCP), which is a natural extension of the horizontal linear complementarity problem studied in Sznajder Degree-theoretic analysis of the vertical and horizontal linear complementarity problems [Ph.D. Thesis. University of Maryland Baltimore County; 1994]. We extend the concepts of R0, R and P pairs from a pair of linear transformations given in Chi et al. The weighted horizontal linear complementarity problem on a Euclidean Jordan algebra. J Global Optim. 2019;73:153–169 to a pair of tensors. When a given pair of tensors has these properties, we use degree-theoretic tools to discuss the existence and boundedness of solutions to the HTCP. Finally, we study a uniqueness result of the solution of the HTCP.
Yadav et al. (Fri,) studied this question.