Hence, the lower cut-off point can be uniquely denoted as ω lower.
the sequence of complex numbers being uniquely fixed, denoting a multiplicative constant.
Let us assume that problem (2.3), (2.4) is uniquely solvable; denote by its Green's matrix and by Green's matrix of the problem (2.1), (2.2).
Hence it has a unique fixed point, denoted, which uniquely solves the fixed point equation (3.3).
From Lan and Wu [17, Theorem ], one sees that has a unique fixed point, denoted, which uniquely solves the fixed point equation (2.13).
Hence, has a unique fixed point, denoted by, which uniquely solves the fixed point equation (2.6).
By the Banach contraction principle, Q t has a unique fixed point, denoted x t, which uniquely solves the fixed point equation (3.1).
By the Banach contraction principle, (Q_{t}) has a unique fixed point, denoted by (x_{t}), which uniquely solves the fixed point equation (3.1).
Then Lemma 1 implies that (T_{t}) has a unique fixed point, denoted by (x_{t}), which uniquely solves the fixed point equation (x_{t} = teta f(x_{t}) + (I-tT UQ_{C}x_{t}).
Then Lemma 1 implies that (T_{t}) has a unique fixed point, denoted by (x_{t}), which uniquely solves the fixed point equation (x_{t} = teta f(x_{t}) + (I-tT Ux_{t}).
for all x, y ∈ H. Hence, it has a unique fixed point, denoted as x t, which uniquely solves the fixed point equation (3.1).
