Equilibrium and mixed equilibrium problems on Hadamard manifolds

Mixed Variational Inequality Interval-valued Problem: Theorems of Existence of Solutions

“…Remark 3.8. (a) Theorem 3.7 generalizes the Existence Theorem 3.1 given by Jiang et al [22] for solutions of variational inequality problem from Banach spaces and Hadamard manifolds to interval-valued functions, Theorem 2.2 given by Jana and Nahak [20], Theorem 3.2 given by Colao et al [9], and Theorem 3.8 given by Jayswal et al [21].…”

“…-We generalized the Existence Theorems for solutions of vector variational inequality problem from Borel and Euclidean spaces given by Jiang et al [22], Jana and Nahak [20], and Jayswal et al [21] to Hadamard manifolds via Fan's lemma. We have illustrated the main results obtained with some examples and numerical results.…”

“…where K is usually assumed to be a nonempty convex set in the real Euclidean space R n , G : K → R n and h : K → R (see [20]).…”

“…(c) If G(x), x − x = F (x, x), then we are in the presence of the mixed equilibrium problem where F be a bifunction satisfying the property F (x, x) = 0 (see [20]).…”

“…In 2016, Jana and Nahak [20] proved the existence of solutions of mixed equilibrium problems on Hadamard manifolds and algorithms that converge to the solution of such problems but not with interval-valued functions.…”