**Volume 10, Issue 8, pp 4085--4098**

**Publication Date**: 2017-08-07

http://dx.doi.org/10.22436/jnsa.010.08.05

Feng Gu - Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.

In this paper, by using the \(w\)-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular \(b\)-metrics. Some new common coupled fixed point theorems are obtained. We also provide illustrative examples in support of our new results. As application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result. The results presented in this paper generalize the well-known comparable results in the literature.

Rectangular b-metric space, coupled coincidence point, common coupled fixed point, w-compatible mapping pairs.

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