The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems in the product spaces of complete quasi-ordered metric spaces. The fixed point theorems in the product spaces will be the special case of coincidence point theorems in the product spaces. We also show that the concept of fixed point theorems in the product spaces extends the concept o...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

Let (φ, ψ) be an (m,n)-valued pair of maps φ, ψ : X ( Y , where φ is an m-valued map and ψ is n-valued, on connected finite polyhedra. A point x ∈ X is a coincidence point of φ and ψ if φ(x) ∩ ψ(x) 6= ∅. We define a Nielsen coincidence number N(φ : ψ) which is a lower bound for the number of coincidence points of all (m,n)-valued pairs of maps homotopic to (φ, ψ). We calculate N(φ : ψ) for all ...

 In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.

Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham 2006 , Lakshmikantham and Ćirić 2009 and many ot...