We introduce and study a generalization of the well-known region of influence proximity drawings, called (ε1, ε2)-proximity drawings. Intuitively, given a definition of proximity and two real numbers ε1 ≥ 0 and ε2 ≥ 0, an (ε1, ε2)-proximity drawing of a graph is a planar straight-line drawing Γ such that: (i) for every pair of adjacent vertices u, v, their proximity region “shrunk” by the multi...

The study of fixed points on the maps fulfilling certain contraction requirements has several applications and been focus numerous research endeavors. On other hand, as an extension idea best approximation, proximity point (ƁƤƤ) emerges. approximation theorem ensures existence approximate solution; is considered for addressing problem in order to arrive at optimum solution. This paper introduce...

In this paper we present a novel approximate algorithm to calculate the top-k closest pairs join query of two large and high dimensional data sets. The algorithm has worst case time complexity OðdnkÞ and space complexity OðndÞ and guarantees a solution within a Oðd1þ1tÞ factor of the exact one, where t 2 {1,2, . . . ,1} denotes the Minkowski metrics Lt of interest and d the dimensionality. It m...

The inability to answer proximity queries efficiently for spaces of dimension d > 2 has led to the study of approximation to proximity problems. Several techniques have been proposed to address different approximate proximity problems. In this paper, we present a new and unified approach to proximity searching, which provides efficient solutions for several problems: spherical range queries, id...

This article investigates some properties of quasi-cyclic and cyclic Jungck modified TS-iterative schemes in complete metric spaces and Banach spaces. In particular, properties of convergence of distances and sequences associated with the self-mappings which define the Jungck modified TS-iterative procedures are studied as well as some properties concerning the convergence of the solution to co...