ON THE STRONG CONVERGENCE OF A GENERAL ITERATIVE ALGORITHM

The paper proves strong convergence of the perturbed hybrid projection algorithm (HPA) under (i)–(iii) and (h1)/(h2) via an implicit–explicit comparison and a Fejér-type energy inequality that avoids non-vanishing drift terms; despite minor typos (δ0* and an “→1” that should be “→0” or α_{n+1}/α_n→1), the argument is complete and correct. By contrast, the model’s one-step estimate introduces a persistent term proportional to α_n‖A(q*)‖, which prevents direct application of the almost-supermartingale lemma; the proposed ‘auxiliary implicit sequence’ fix is not actually developed, leaving a gap. See the statement of Theorem 4.1 and its proof, including Lemma 3.2 and the key estimates for yn and xn−yn, in the paper’s Sections 3–4 .