Sehgal-Guseman-Type Fixed Point Theorems In B-(Rectangular) Metric Spaces

This thesis mainly studies Sehgal-Guseman-type fixed point theorems in generalized metric spaces.It is mainly divided into two parts:one is the Sehgal-Gusemantype fixed point theorem in b-rectangular metric space,and the other is the SehgalGuseman-type common fixed point theorems in b-metric space.In b-rectangular metric space,an open question,proposed by Mitrovic in 2018,is solved in this thesis.In order words,this thesis proves the Sehgal-Guseman-type fixed point theorem in b-rectangular metric space.Indeed,this theorem generalizes and unifies some fixed point theorems in generalized metric spaces.In b-metric spaces,by constructing counterexamples,this thesis points out that the conclusion of alqahtani et al.on Sehgal-Guseman-type common fixed point in b-metric spaces is wrong.This thesis gives two corresponding Sehgal-Guseman-type common fixed point theorems and their proofs to correct them.