Monotone iterative technique and connectedness of the set of solutions

TL;DRAbstract

Let B be ah ordered Banach space with an order cone P,UcB and let A: U ~» U be a continuous operator.The operator A is order preserving if x < y =*• A(x) ^ A(y), strictly order preserving if x < y =*-A(s) < -4(y), strongly order preserving if a; < y => .4(2;)<C A(j/).(a; <£ y means y -x e intP.)An element x e U is called a subequilibrium (superequilibriurn) provided x <_ Ax (x >• Ax).A sub-or superequilibriurn is called strict if the strict inequality holds.We denote [v,w] = {u e B; v <_ u <_ w}.

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