UPPER BOUNDS FOR VECTOR EQUILIBRIUM PROBLEMS ASSOCIATED WITH p-ORDER CONE ON HADAMARD MANIFOLDS

In this paper, we study a new class of vector equilibrium problems associated with partial order provided by p-order cone on Hadamard manifolds. We first propose a new concept of K-p(k)-convexity of a vector-valued function in the setting of Hadamard manifolds and derive some regularized gap functions of the concerning problem. Then, several upper bounds for vector equilibrium problems associated with p-order cone are established via regularized gap functions. At last, we present some examples to illustrate our main results in the paper.