In this paper we introduce the concept of cone metric spaces with Banach algebras, replacing Banach spaces by Banach algebras as the underlying spaces of cone metric spaces. With this modification, we shall prove some fixed point theorems of generalized Lipschitz mappings with weaker conditions on generalized Lipschitz constants. An example shows that our main results concerning the fixed point theorems in the setting of cone metric spaces with Banach algebras are more useful than the standard results in cone metric spaces presented in the literature. MSC: 54H25; 47H10

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We introduce the concept of quasicontractions on cone metric spaces with Banach algebras, and by a new method of proof, we will prove the existence and uniqueness of fixed points of such mappings. The main result generalizes the well-known theorem of Ćirić (Ćirić 1974).

The level of urbanization is a key factor in urban development. In this study, to better characterize the level of urbanization, the panel entropy weight method is used to weight the factors of population, industry, and area to construct a composite indicator of urbanization. A panel regression between this composite index and the average night light values after fusion shows a strong correlation. An accuracy test indicates that the estimated value of fused average light as calculated by the urbanization level estimation model that adequately represents the urbanization level. On this basis, night light data is corrected for zero error on the pixel scale, and spatiotemporal evolution analyses are performed on the city and county scales. The standard deviation ellipse method is used to find that the spatial distribution pattern of the Beijing-Tianjin-Hebei urbanization level from 1995 to 2018 radiates and spreads to the northeast, with Beijing-Tianjin as the center. The spatial pattern shows a contracting trend that is strengthening year by year. Slope analyses show that areas with rapid urbanization growth are mainly concentrated in Beijing and Tianjin. The urbanization development speed of most counties in the Hebei Province is at a low level.

Opportunities faced by China’s sports industry in the era of big data are as follows: the mining and analysis of big data creates more value for the sports industry; promotes the coordinated innovation and development of sports industry clusters; and accelerates the technological progress of the sports industry. This is both an opportunity and a challenge for the sports industry. At present, the following problems still exist in sports industry: lack of human resources to complete advanced data management and development in sports industry; difficulties in data storage in sports industry; inadequate depth of data mining in sports industry; difficulty in guaranteeing user information and privacy; strong competitiveness of foreign-funded enterprises to domestic enterprises. Some countermeasures are put forward, such as solving the problem of sports big data storage, improving the ability of big data processing and service, introducing advanced data processing manpower, building scientific research team, protecting personal privacy, and doing a good job of sports industry collaborative innovation research.

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Infectious diseases are common challenges faced by people around the world, which jeopardize public health, as well as human well-being in various aspects of social and economic development. Although much progress has been made in spatial epidemiology, there is still very little scientific understanding of knowledge domain mapping with scientometric analysis. Based on a total of 4,552 literature records collected from the Web of Science Core Collection™, quantitative changes, research frontiers, research hotspots, and collaboration networks were analyzed by CiteSpace. The results show that both total publications and sum of times cited per year exhibit a rapid development trend in recent decades. The USA, England, and France are highly active in the field. The network of documents co-citation analysis is validated with almost same importance of documents, and primary research frontiers are landscape genetics, modeling and spatial analysis, and tropical diseases. The clustering of the keywords co-occurrence analysis network is heterogeneous and highly reliable, and research hotspots are related to phoma stem canker, vector preference, and aerosol chemical component. Scholars in the field of spatial epidemiology are closely connected, and they have been in a stable cooperative network, as well as institutions. Overall, scientometric analysis based on CiteSpace provides a sound tool to better understand the frontiers, hotspots, and emerging trends in the research domain of spatial epidemiology.