In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...

This paper deals with topical and sub-topical functions in a class of ordered Banach spaces. The separation theorem for downward sets and sub-topical functions is given. It is established some best approximation problems by sub-topical functions and we will characterize sub-topical functions as superimum of elementary sub-topical functions.

We study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

we study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

BACKGROUND/AIMS To devise and evaluate a novel Ocular Anaesthetic Scoring System (OASS) for non-topical local anaesthesia. METHODS In OASS, a score of between 0 (poor) and 14 (excellent) was devised measuring motor (ocular motility, levator and orbicularis function) and sensory functions (digital spear pressure at limbus and topical anaesthetic sting). 40 patients were studied prospectively t...

BACKGROUND Several local anaesthetic techniques are available for cataract surgery. Recently, topical anaesthesia has gained in popularity. A randomized trial was designed to compare patient discomfort and intraoperative complications following routine cataract surgery under topical or sub-Tenon's anaesthesia. METHODS A randomized double-blinded placebo-controlled clinical trial of 210 patien...