In the present investigation we introduce some subclasses of the function class Σ of bi-univalent functions defined in the open unit disk U, which are associated with the quasi-subordination. We obtain the estimates on initial coefficients |a 2 | and |a 3 | for the functions in these subclasses. Also several related subclasses are considered and connection with some known results are established.
Context:Peripheral anterior synechiae (PAS; synechiae anterior to functional trabecular meshwork) formation in primary angle-closure glaucoma (PACG) hampers access to uveoscleral outflow. Thus, the role of bimatoprost in such patients with 360° synechiae was evaluated.Aims:To assess efficacy and safety profile of bimatoprost 0.03% in lowering intraocular pressure (IOP) in 360° synechial angle-closure glaucoma patients.Settings and Design:This was a prospective, non-randomized, non-comparative, selective analysis, single-center pilot study.Materials and Methods:A total of 23 eyes of 20 Indian chronic angle-closure glaucoma (CACG) patients with IOP greater than 21 mmHg, 360° PAS and no visual potential in the study eye underwent detailed eye examination. Baseline IOP was measured and YAG peripheral iridotomy was performed for complete angle-closure reconfirmation. Bimatoprost 0.03% was administered for 8 weeks as once-daily evening dose. IOP reduction within treatment group was determined with “paired t-test”.Results:The mean reduction in IOP from baseline to 8 weeks of bimatoprost therapy was 15.3 ± 9.5 mmHg (P < 0.001). The most commonly observed adverse event was conjunctival hyperemia (35%). Bimatoprost was well tolerated in the study.Conclusions:In this study, exclusively involving patients with 360° synechial angle-closure glaucoma and no visual potential, bimatoprost 0.03% treatment demonstrated a statistically significant IOP reduction. Hence, it can be inferred that bimatoprost 0.03% is an efficacious treatment modality in this subgroup of patients for reducing IOP.
Abstract:In recent years, the study of bi-univalent functions have gathered momentum mainly due to the pioneering work of Srivastava et al. [19], which has actually revived the study of the coefficient problems involving bi-univalent functions. With motivation from the work of Srivastava et al. [19], in the present paper we introduce a new subclass T Σ [φ ] of the function class Σ of bi-univalent functions defined in the open unit disk U = {z ∈ C : |z| < 1}. Further, for the functions in this subclass T Σ [φ ] we obtain bounds on |a 2 |, |a 3 | and |a 4 |.
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