“情境引入探究教学法”的理论与实践

文章构建了“数学文化”教学新方法——“情境引入探究教学法”,契合了教育纲要“培养复合型人才”的新理念,顺应了新时代“传播数学文化”的新要求,创新了高等院校“数学文化”教学模式,开辟了一条“情境引入—自主探究—总结点评—拓展延伸—内化提升”的新型“数学文化”教学之路。该教学法以教师“情境引入”为导向,以学生“自主探究”为核心,以提升学生“数学素养”为目的,具有鲜明的时代性、高度的融合性、典型的创新性和较强的可操作性,适用于本科院校“数学文化”课程教学。

Topological degree for 1-set-contractive fields in M-PN spaces and its applications

In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.

1-set-contractive perturbations of accretive operators in Menger PN-spaces

Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.

Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces

In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.