In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a mixed equilibrium problem, a general system of variational inequalities and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. MSC: 49J30; 47H10; 47H15

Background Trajectories of pulse oxygen saturation (SpO2) within the first few days after birth are important to inform the strategy for identifying asymptomatic hypoxemic disease but remain poorly substantiated at higher altitudes. Methods We performed a longitudinal cohort study with consecutive neonates at a local hospital in Luchun County, China, at an altitude of 1650 m between January and July 2020. We repeatedly measured the pre- and post-ductal SpO2 values at 6, 12, 18, 24, 36, 48, and 72 hours after birth for neonates without oxygen supplements. All neonates underwent echocardiography and were followed up to 42 days after discharge. We included neonates without hypoxemic diseases to characterize the trajectories of SpO2 over time using a linear mixed model. We considered the 2.5th percentile as the reference value to define hypoxemic conditions. Results A total of 1061 neonates were enrolled. Twenty-five had non-cardiac hypoxemic diseases, with 84% (21/25) presenting with abnormal SpO2 within 24 hours. One had tetralogy of Fallot identified by echocardiography. Among the 1035 asymptomatic neonates, SpO2 values declined from 6 hours after birth, reached a nadir at 48 hours, and tended to level off thereafter, with identical patterns for both pre- and post-ductal SpO2. The reference percentile was 92% for both pre- and post-ductal SpO2 and was time independent. Conclusions A decline within 48 hours features SpO2 trajectories within the first 72 hours at moderate altitude. Our findings suggest that earlier screening may favorably achieve a benefit–risk balance in identifying asymptomatic hypoxemic diseases in this population.

In this paper, we introduce a new class of generalized strict pseudocontractions in a real Hilbert space, and we consider a three-step Ishikawa-type iteration method