The existence of coincidence and fixed points for continuous mappings in compact Hausdorff spaces is established. Some equivalent conditions of the existence of fixed and common fixed points for any continuous mapping and a pair of mappings in compact Hausdorff spaces are given, respectively. Our results extend, improve, and unify the corresponding results due to Jungck, Liu, and Singh and Rao.

In this paper we investigate the following problem (see I.A. Rus, Fixed Point Structure Theory, Cluj Univ. Press, Cluj-Napoca, 2006, pp. 193-194): Let X be a set with structure and (X,S(X),M) be a large fixed point structure on X. Let U ∈ S(X). An operator p : U → U is by definition coincidence producing operator on (X,S(X),M) if for each f ∈M(U) there exists u ∈ U such that f(u) = p(u). The pr...

In this paper, coupled xed point results of Bhaskar-Lakshmikantham type [T. Gnana Bhaskar, V.Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, NonlinearAnalysis 65 (2006) 1379-1393] are extend, generalized, unify and improved by using monotonemappings instead mappings with mixed monotone property. Also, an example is given to supportthese improvements.

In this note we point out and rectify some errors in a recently published paper “N. Singh, R. Jain: Coupled Fixed Point Results For Weakly Related Mappings In Partially Ordered Metric Spaces, Bull. Iranian Math. Soc. 40 (2014), no. 1, 29-40”.

In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. 2011 . Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partial...