A convexity of functions on convex metric spaces of Takahashi and applications

We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions on these spaces and refer to it as $W-$convexity. $W-$convex functions generalize convex functions on linear spaces. We discuss illustrative examples of (strict) $W-$convex functions and dedicate the major part of this paper to proving a variety of properties that make them fit in very well with the classical theory of convex analysis. Finally, we apply some of our results to the metric projection problem and fixed point theory

A New Combination Formula for Treatment of Fungal Keratitis: An Experimental Study

Objective. To formulate and evaluate slow release ketoconazole and ketorolac to treat fungal keratitis and associated inflammation. Methods. Experimental study with the following outcome measures. Pharmaceutical Evaluation. Mucoadhesive gels containing ketoconazole and ketorolac were used. Microbiological in vitro evaluation was performed using cup method. In vivo evaluation was performed on 24 rabbits divided into 2 groups, 12 rabbits each, group A (fast release formula; 6 times daily) and group B (slow release formula; 3 times daily). Each group was divided into two subgroups (6 rabbits each). Both eyes of rabbits were inoculated with Candida albicans. The left eye of all rabbits received the combination formulae. The right eye for one subgroup received ketoconazole as control 1 while the other subgroup received placebo as control 2. Clinical follow-up was done and, finally, the corneas were used for microbiological and pathological evaluation. Results. Gels containing high polymer concentration showed both high viscosity and mucoadhesion properties with slower drug release. The infected eyes treated with slow release formula containing both drugs showed better curing of the cornea and pathologically less inflammation than eyes treated with fast release formula. Conclusion. Slow release formula containing ketoconazole and ketorolac showed higher activity than fast release formula against fungal keratitis and associated inflammation