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The notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior and De la vallée Poussin mean of a single integral. Moreover, some remarks and corollaries are provided here to support our theorems.

Purpose To study long-term visual and refractive outcomes and complications in eyes with anterior chamber intraocular lens (ACIOL) implantation. Methods Data of patients who underwent primary and secondary ACIOL implantation at L V Prasad Eye Institute, Bhubaneswar between 2011 and 2020 was collected, including details of post-operative visits. For analysis, sample was divided into: group Ia (primary ACIOL in cases without risk factors, n = 104); group Ib (primary ACIOL in cases with pre-existing risk factors, n = 49); and group II (secondary ACIOL, n = 40). Results A total of 193 eyes of 192 patients were included. Mean post-operative follow-up in groups I and II were 8.6 and 11.51 months, respectively. Mean pre-operative and last visit corrected distance visual acuity were 1.73 ± 0.11 and 0.42 ± 0.05 logMAR units in group Ia (p \ 0.001), and 1.53 ± 0.14 and 0.49 ± 0.10 logMAR units in group Ib (p \ 0.001). The mean spherical equivalent (MSE) for last refraction was -0.37 ± 0.18 diopters (D) and -0.15 ± 0.51 D in groups I and II, respectively. Of 76 eyes in which addition of 2.5 D (over the near emmetropic posterior chamber intraocular lens power) was taken for ACIOL, 40 (52.6%) had MSE within ± 0.5 D. Most common complications were transient corneal edema and anterior chamber reaction. Eyes on anti-glaucoma medications at last visit were eight (7.7%), 15 (30.6%), and two (5.0%) in groups Ia, Ib, and II, respectively. Conclusion We observed that ACIOLs have good visual and refractive outcomes. Raised IOP is a concern in eyes with pseudoexfoliation, but can be managed with close monitoring. Hence ACIOL can be a good option for managing aphakia after cataract surgery.