the purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fi xed point on geraghty-contraction. in this paper,de nitions of approximate -pair fi xed point for two maps tα , sα and theirdiameters are given in a metric space.

Abstract. This paper presents an efficient and sufficient algorithm to approximate general interpolating Spline curve which goes through the given set of design-data points by using asymptotic iterative B-spline curves. Firstly, the given set is considered as the control points of a B-spline, to create the initial approximate curve, then the iterative grade is built based on the error between t...

We suggest a simple modification to the Kd-tree search algorithm for nearest neighbor search resulting in an improved performance. The Kd-tree data structure seems to work well in finding nearest neighbors in low dimensions but its performance degrades even if the number of dimensions increases to more than two. Since the exact nearest neighbor search problem suffers from the curse of dimension...

We consider computing the saddle points of a convex-concave function using subgradient methods. The existing literature on finding saddle points has mainly focused on establishing convergence properties of the generated iterates under some restrictive assumptions. In this paper, we propose a subgradient algorithm for generating approximate saddle points and provide per-iteration convergence rat...

Range searching is among the most fundamental and well-studied problems in computational geometry. Given an n-element point set in R, the problem is to preprocess the points so that the total weight, or generally the semigroup sum, of the points lying within a given query range η can be determined quickly. Years of research have resulted in nearly matching upper and lower bounds for many formul...