Meir and Keeler in 1 considered an extension of the classical Banach contraction theorem on a complete metric space. Kirk et al. in 2 extended the Banach contraction theorem for a class of mappings satisfying cyclical contractive conditions. Eldred and Veeramani in 3 introduced the following definition. Let A and B be nonempty subsets of a metric space X. A map T : A ∪ B → A ∪ B, is a cyclic co...

We prove: For all n and all n-cylic isometriesφ : ΛQ → ΛQ of the rational K3 lattice there exists an algebraic realization of φ, i.e. marked algebraic K3 surfaces (S,ηS) and (M,ηM), whereM is a moduli space of sheaves on S, and a Hodge isometry ψ : H2(S,Q)→ H2(M,Q) such that φ = ηM ◦ψ ◦ η−1 S . 1 Facts about cyclic isometries We need the existence of a triple ((S,ηS), (M,ηM),ψ) to have a point ...

Endpoint results are presented for multi-valued cyclic contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Nadler (1969), Daffer-Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

In this paper, we present best proximity point theorems for new class ofK−rational proximal contraction, in the setting of metric spaces. Some illustrative example are also given.