Random quadruple coincidence points theorems for sequence of random mappings and application

In this paper, we give the definitions of compatibility and weakly reciprocally continuity for sequence of random mappings g and a random selfmapping g. Further, using these definitions we establish quadruple random coincidence and quadruple random fixed point results by applying the concept of an α-series for sequence of mappings, introduced by Sihag et al. [V. Sihag, R. K. Vats, C. Vetro, Quaest. Math., 37 (2014), 16], in the setting of partially ordered metric spaces. Our results are some random versions and extensions of results relating to triple fixed points theorems by R. K. Vats et al. [R. K. Vats, K. Tas, V. Sihag, A. Kumar, J. Inequal. Appl., 2014 (2014), 12 pages], we also give some examples to illustrate our results.