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In this paper, we introduce the concept of compatible and compatible mapping of type (A) in G-metric space akin to compatible and its type (A) in metric space introduced by Jungck [7] and Jungck et.al [8] and then establishes an example to show their independency. Further, we prove a common fixed point theorem for two pair of expansive mappings which generalize and unify the results of Wang et.al. [19] and Daffer et.al. [17]. Examples are given to support the generality of our result. Finally, we elaborate our theorem as an application in product space. Keywords: G-metric space, fixed point, compatible mapping of type (A) and ϕ function of contractive modulus.

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) 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

In this article, we propose two Banach-type fixed point theorems on bipolar metric spaces. More specifically, we look at covariant maps between bipolar metric spaces and consider iterates of the map involved. We also propose a generalization of the Banach fixed point result via Caristi-type arguments.

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