... be used in the proofs for the main results in the next section.Let H be a real Hilbert space with inner product ·, · and norm ·, respectively.It is wellknown that for all x, y ∈ H and λ ... with a constant β ∈ 0, 1 and letB be a strongly bounded linear operator on H with coefficientγ>0 and 0 <γ<γ/β.Let{βkn} be afamily of nonnegative numbers with indices n, k ∈ N with ... is monotone, that is, Fx, yFy, x ≤ 0 for all x, y ∈ C;A3 for each x, y, z ∈ C,limt → 0Ftz 1 − tx, y≤ Fx, y; 2.4A4 for each x ∈ C, y → Fx, y is convex and...