Some further studies on strong ℐλ-statistical convergence in probabilistic metric spaces

We prove some basic properties of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence of sequences in probabilistic metric spaces and introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical cluster point. We also introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences in probabilistic metric spaces. Further, we establish a connection between strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence and strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences.

On I-statistically limit points and I-statistically cluster points of sequences of fuzzy numbers

The main aim of this paper is to introduce I-st limit points and I-st cluster points of a sequence of fuzzy numbers and also study some of its basic properties. Conditions for a I-st limit point of a I-st cluster point are investigated.

Impact of Imprecise Household Location on Effective Coverage Estimates Generated through Linking Household and Health Provider Data by Geographic Proximity

Background: Combining household and health provider data can be used to estimate coverage of interventions and identify barriers to use. Without data on specific sources of care utilized by individuals, researchers often assign individuals to healthcare providers based on geographic proximity. The Demographic and Health Survey (DHS), a common source of population health data, does not collect data on the location of participant households. They present displaced data on the central point within household clusters. This may introduce error into analyses based on the distance between households and providers. Methods: We assessed the effect of imprecise household location on quality-adjusted effective coverage of child curative services estimated by linking sick children to providers based on geographic proximity. We used data on care-seeking for child illness and health provider quality in Southern Province, Zambia. The dataset included the location of respondent households, a census of providers, and data on the exact outlets utilized by sick children included in the study. We displaced the central point of each household cluster point five times. We calculated quality-adjusted coverage by assigning each sick child to a provider’s care based on three measures of geographic proximity (absolute distance, travel time, and geographic radius) from the household location, cluster point, and displaced cluster locations. We compared the estimates of quality-adjusted coverage to each other and estimates calculated using each sick child’s true source of care. Results: Fewer children were linked to their true source of care using cluster locations than household locations. Estimates of coverage were not statistically different using different measures of geographic proximity or household location. Estimates did not vary significantly from estimates produced using each sick child’s true source of care. Conclusions: Use of original or displaced cluster location did not produce statistically different coverage estimates than using household location. However, it did reduce the proportion of children that linked to their true source of care. The limited effect of household location imprecision on quality-adjusted coverage estimates could be due to a lack of variability in provider quality. These findings may not hold in a setting with more considerable variation in provider quality. This work was supported by the Bill & Melinda Gates Foundation, Grant Number INV-006966

On n-Convergence of Filters

In this work, we have present a new form of sets named - open sets. We have study and described some of the properties and relationships between these sets. We have obtained some results and relationships between by the theories inferring through the style set (n-open). Furthermore, we presented an analysis of the classes of convergence in topological spaces. We called it a name n convergence of filters beneficiaries of the idea of -open sets and its possibilities of - cluster point of filters has been studied.