Abstract
The scientific and theoretical approaches to the study of convergence theories are analyzed and summarized in the article. Feasibility of updating process of territorial convergence of economic systems with differential features of development is outlined. It is proved a necessity of developing a promising concept for the development of rural border areas, which will promote sustainable development based on the consideration of socio-economic, natural and environmental characteristics of the area. In this study the theories and concepts of convergence will enable to detect individual weaknesses and identify the causes affecting the efficiency of providing perspective development of rural border areas. It is proved that in order to ensure convergence processes of rural border areas must be considered above all productivity of land resources, because the land is an important part of rural development. It is proved a necessity of implementation of new approaches to the management of economic development that will promote regional convergence systems.
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