Generalizations Of Some Fixed Point Theorems For Nonlinear Quasi-contractions

The fixed point theorems in many branches of mathematics have a wide range of applications.The extentions and applications of fixed point theorems are discussed for nonlinear quasi-contraction mappings in uniform spaces and dislocated quasi-b-metric spaces.The main works are as follows.1.In uniform spaces,we introduce the concepts of generalized q-distances(particu-larly,generalized p-distances)and sequential completeness with respect to a generalized q-distance.By using generalized q-distances and the new type of completeness,we estab-lish a fixed point theorem for mappings satisfying(?,?,p)-weakly contractive conditions in uniform spaces.The theorem presented extends and generalizes the recent result of Lakzian et al.in 2013.2.We give a notion of nonlinear quasi-contraction mapping of (?)iri(?)-type and estab-lish a common fixed point theorem including its mapping on dislocated quasi-b-metric spaces.This result extends the result of He et al.from dislocated quasi-metric spaces to dislocated quasi-b-metric spaces.Meanwhile,the result of Amini-Harandi in b-metric spaces is obtained,where the condition of Fatou property may be omitted.As an appli-cation,we establish a common fixed point theorem for a nonlinear quasi-contraction of(?)iri(?)-type in quasi-partial b-metric spaces.3.In 2015,Singh et al.gave a one mapping generalization fixed point theorems for weakly contractive version of Suzuki type.This result extend some results of Doric,Zhang et al.and others.Meanwhile,they advance a conjecture about two mappings fixed point.In this paper,we give a proof of the conjecture of Singh et al.and answer their question.