Some common fixed point theorems in metric spaces under a different set of conditions


Mohammad Imdad, Anupam Sharma, Sunny Chauhan




The purpose of this paper is to prove some new common fixed point theorems in metric spaces for weakly compatible mapping satisfying an implicit relation under a different set of conditions, which unify and generalize most of the existing relevant fixed point theorems. While proving our results, we utilize an implicit function due to Popa et al. [Using implicit relations to prove unified fixed point theorems in metric and $2$-metric spaces. Bull. Malays. Math. Sci. Soc. (2) 33 (1) (2010), 105-120] keeping in view their unifying power. Our results improve some recent results contained in Imdad and Ali [Jungck's common fixed point theorem and (E.A) property. Acta Math. Sinica, Eng. Ser. 24(1) (2008), 87-94]. Some related results and illustrative examples to highlight the realized improvements are also furnished.