COMMON FIXED POINTS OF TWO PAIRS OF SELFMAPS SATISFYING A GERAGHTY-BERINDE TYPE CONTRACTION CONDITION IN b-METRIC SPACES
Vol. 9(2) July 2021, No. 2, pp. 12-36
K.BHANU CHANDER AND T.V. PRADEEP KUMAR
In this paper, we introduce Geraghty-Berinde type contraction for two pairs of selfmaps in b-metric spaces and we prove the existence of common fixed points under the assumptions that these two pairs of maps are weakly compatible and satisfying a Geraghty-Berinde type contraction condition in complete b-metric spaces. The same is extended to a sequence of selfmaps. Also, we prove the same with different hypotheses on two pairs of selfmaps in which one pair is compatible, reciprocally continuous and the other one is weakly compatible. Further, we also prove the same with different hypotheses on two pairs in which these selfmaps are satisfy b-(E.A)-property. We also discuss the importance of L in our contraction condition. Our theorems extend/generalize some of the results in literature to two pairs of self maps.