(G, F)-Closed set and tripled point of coincidence theorems for generalized compatibility in partially metric spaces - Charoensawan,P. (Springer Publishing Company, 2015)
In this work, we prove the existence of a tripled point of coincidence 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 G-increasing property of F and mixed monotone property of G, using the concept of a [InlineEquation not available: see fulltext.]-closed set. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of tripled coincidence point by G using the mixed monotone property. We also show the uniqueness of a tripled point of coincidence of the given mapping. Further, we apply our results to the existence and uniqueness of a tripled point of coincidence of the given mapping with G-increasing property of F and mixed monotone property of G in partially ordered metric spaces. © 2014 Charoensawan and Thangthong; licensee Springer.