This study examines the impact of education quality and innovative activities on economic growth in Shanghai through international trade and fixed asset formation. The study examines how higher education quality and innovation activities drive regional economic growth, with a focus on the mediating effects of international trade and fixed asset formation in Shanghai. The study adopts a quantitative approach utilizing panel data from 31 provinces in China covering the period from 1999 to 2022. The study incorporates variables such as education quality, innovation capacity, and GDP per capita, as well as control variables like labor, capital, and infrastructure. The methodology involves multiple regression models and robustness tests to verify the relationships between and effects of education quality and innovation with regard to economic growth. This study analyzes the direct and indirect effects of university R&D expenditure and innovation on economic growth using a regression model, based on data from 2014 to 2022 in relation to Shanghai. The model introduces variables such as international trade, capital formation, and urbanization to analyze the relationship between higher education quality and economic growth.

The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.