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The ICT service industry has become a burgeoning industry at a high and stable speed. Their equitable distribution can improve national and global positive peace. This paper aimed to verify the characteristics of spatio-temporal evolution and its influencing factors in the ICT service industry. Based on the data from 31 Provinces in China from 2015 to 2019, this paper uses location quotient, spatial autocorrelation methods and spatial econometric analysis to explore the development characteristics, evolution and influencing factors of the ICT service industry, respectively. The main results are shown as follows: (1) China's ICT service industry is mainly concentrated in Beijing, Shanghai, Zhejiang, Tibet, and Guangdong, with a trend of specialisation development. They are not only distributed in cities with relatively superior overall development but also those with superior industrial and development carrier elements. Technological relevance, aggregation, and political difference might have an impact on promoting the emergence and development of these industries. (2) ICT service industry is characterised by stable and highly concentrated development. Numbers between three to five significant provinces and types with high-high (HH) and high-low (HL) clusters of local spatio-temporal association kept stable in the period. The HH was in eastern coastal areas, including Zhejiang, Shanghai, Jiangsu, and Shandong, and the HL was in Guangdong in 2015. There is a definite spatial correlation in spatial distribution with constant strengthening. (3) TUR, NDN, MIAT and the area were shown to have a significant role in promoting the ICT service industry, while NW, GDP and ICT Employment were shown to have a significant negative impact on this industry. Correspondingly, two strategies were put forward here: (1) accelerating the inter-provincial networking development of the ICT service industry, and (2) strengthening government policy guidance for the ICT service industry. These outcomes can not only provide a scientific basis and theoretical support for the distribution of strategies and resources for these industries at the theoretical level but also improve resource integration from the national perspective and the efficiency of resource use at the practical level. [ABSTRACT FROM AUTHOR]

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dual cone in Hilbert spaces. We first discuss the relation between the isotonicity of the projection onto the cone and its dual cone. Some sufficient conditions for the isotonicity of the projection with respect to the mutually dual orders onto general cones are then proved. By using the self-dual cone in the hyperplane, we establish some specific isotone projection cones. Some properties and representations of the projection onto these cones are studied. We also prove some heredity and expansivity for the isotonicity of the projection onto these cones. By using the isotonicity characterizations of the projection with respect to the mutually dual orders, some solvability and approximation theorems for the complementarity and conic optimization problems are obtained. In Theorems 5.1–5.4, if the order relation does not satisfy the regularity, to guarantee convergence of isotone Picard iterations, three different order methods are used, respectively. Our results generalize those about the isotone projection cone and methods to establish isotone iterations for complementarity problems. [ABSTRACT FROM AUTHOR]