$\alpha$-SERIES FOR QUADRUPLED FIXED POINT

Abstract

This manuscript has two aims: rst we extend the denitions of compatibility and weakly reciprocally continuity, for a quadvariate 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 denitions we establish quadrupled coincidence and xed point results by applying the new concept of an -series for sequence of mappings, introduced by Sihag et al. (Quaest. Math. 37:1-6, 2014), in the setting
of partially ordered metric spaces.