Numerical Simulation On Blasting Cavity And Experimental Study Of Grouting For Supporting In Soil

A quasi-metric is a distance function which is not necessarily satisfying symmetry.The fundamental theory of quasi-metric spaces is widely used in the field of multi-objective constrained optimization,artificial intelligence,nonlinear control,theoretical computer,etc..In this paper,we generalize the classic Ekeland variational principle and Caristi's fixed point theorem of metric spaces into quasi-metric spaces.In addition,we study some collinear problems,start point problems and fixed point problems on quasi-metric spaces,mainly including the following aspects:1.We prove a quasi-metric version of Ekeland variational principle of a bifunction using the closed set theorem on quasi-metric spaces.In addition,we give the minimal theorem in a partially ordered set which can prove the Caristi's fixed point theorem of the single valued situation as its applications.2.We introduce relative notions of pseudo-quasi-metric interval in pseudo-quasi-metric spaces.Based on that,collinear problems and start point problems are also considered on the pseudo-quasi-metric spaces.Moreover,a fixed point theorem of the set-valued situation,a fixed point theorem for directional contractions and a common fixed point theorem have been proved.