[InlineEquation not available: see fulltext.]-Closed set and coupled coincidence point theorems for a generalized compatible in partially G-metric spaces - Na Nan N. (Springer Publishing Company, 2015)
© 2014, Na Nan and Charoensawan; licensee Springer. In this work, we present a notion of an [InlineEquation not available: see fulltext.]-closed set and prove the existence of a coupled coincidence point theorem for a pair [InlineEquation not available: see fulltext.] of mappings [InlineEquation not available: see fulltext.] with φ-contraction mappings in partially ordered metric spaces without H-increasing property of F and mixed monotone property of H. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by H using the mixed monotone property and H-increasing property of F. We also show the uniqueness of a coupled coincidence point of the given mappings. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mappings in partially ordered G-metric spaces with H-increasing property of F and mixed monotone property of H. These results generalize some recent results in the literature.