A New Exceptional Family of Elements and Solvability of General Order Complementarity Problems

الملخص EN

By using the concept of exceptional family, we proposea sufficient condition of a solution to general order complementarity problems (denoted by GOCP) in Banach space, which is weaker than that in Németh, 2010 (Theorem 3.1).

Thenwe study some sufficient conditions for the nonexistence of exceptional family forGOCP in Hilbert space.

Moreover, we prove that without exceptional family isa sufficient and necessary condition for the solvability of pseudomonotone generalorder complementarity problems.