Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces

We introduce a generalized proximal weak contraction of rational type for the non-self-map and proved results to ensure the existence and uniqueness of best proximity point for such mappings in the setting of partially ordered metric spaces. Further, our results provides an extension of a result due to Luong and Thuan (2011) and also it provides an extension of Harjani (2010) to the case of self-mappings

Best proximity points of p-cyclic orbital Meir–Keeler contraction maps

Let (X,d) be a metric space and A1, A2, ..., Ap be nonempty subsets of X. We introduce a self map T on X, called p-cyclic orbital contraction map on the union of A1, A2, ..., Ap and obtain a unique best proximity point of T. That is, a point x ∈ ∪i=1pAi such that d(x,Tx) = dist(Ai, Ai+1), 1 ≤ i ≤ p, where dist(Ai, Ai+1) = inf d(x,y: x ∈ Ai, y ∈ Ai+1)

The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space

We prove the existence and uniqueness of coupled best proximity point for mappings satisfying the proximally coupled contraction in a complete ordered metric space. Further, our result provides an extension of a result due to Bhaskar and Lakshmikantham

The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space

We prove the existence and uniqueness of coupled best proximity point for mappings satisfying the proximally coupled contraction in a complete ordered metric space. Further, our result provides an extension of a result due to Bhaskar and Lakshmikantham