Triple fixed point theorems via α-series in partially ordered metric spaces

Abstract

Abstract This manuscript has two aims: first we extend the definitions of compatibility and weakly reciprocally continuity, for a trivariate mapping F and a self-mapping g akin to a compatible mapping as introduced by Choudhary and Kundu (Nonlinear Anal. 73:2524-2531, 2010) for a bivariate mapping F and a self-mapping g. Further, using these definitions we establish tripled coincidence and fixed point results by applying the new concept of an α-series for sequence of mappings, introduced by Sihag et al. (Quaest. Math. 37:1-6, 2014), in the setting of partially ordered metric spaces. MSC:54H25, 47H10, 54E50.