In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditionsabout co-farthest points and dual space. Also, we show that everyco-remotal set is co-uniquely set. پرونده مقاله

In this paper, we introduce a cone generalized semi-cyclic$\varphi-$contraction maps and prove best proximity points theorems for such mapsin cone metric spaces. Also, we study existence and convergence results ofbest proximity points of such maps in normal cone metric spaces. Our resultsgeneralize some results on the topic. پرونده مقاله

In this paper we define fuzzy farthest points, fuzzy best approximation points and farthest orthogonality in fuzzy normed spaces and we will find some results. We prove some existence theorems, also we consider fuzzy Hilbert and show every nonempty closed and convex subset of a fuzzy Hilbert space has an unique fuzzy best approximation.It is well know that the conception of fuzzy sets, firstly defined by Zadeh in 1965. Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. The theory of fuzzy sets has become an area of active research for the last forty years. On the other hand, the notion of fuzzyness has a wide application in many areas of science and engineering, chaos control, nonlinear dynamical systems, etc. In physics, for example, the fuzzy structure of space time is followed by the fat that in strong quantum gravity regime space time points are determined in a fuzzy manner. پرونده مقاله

Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed linear space X and S,T : A∪B → A∪B be two cyclicmappings. Let (A,B) be a nonempty pair in a normed linear space X andS,T : A∪B → A∪B be two cyclic mappings. A point p ∈ A∪B is called acommon best proximity point for the cyclic pair (T,S) provided that∥p − Tp∥ = d(A,B) = ∥p − Sp∥In this paper, we survey the existence, uniqueness and convergence of a com-mon best proximity point for a cyclic weak ST − ϕ-contraction map, whichis equivalent to study of a solution for a nonlinear programming problem inthe setting of uniformly convex Banach spaces. We will provide examples toillustrate our results. پرونده مقاله

In this paper, we consider Nearest points" and Farthestpoints" in normed linear spaces. For normed space (X; ∥:∥), the set W subset X,we dene Pg; Fg;Rg where g 2 W. We obtion results about on Pg; Fg;Rg. Wend new results on Chebyshev centers in normed spaces. In nally we deneremotal center in normed spaces. پرونده مقاله

‎A kind of approximation‎, ‎called best coapproximation was‎ introduced and discussed in normed linear spaces by C‎. ‎Franchetti and M‎. Furi in 1972‎. ‎Subsequently‎, ‎this study was taken up by several researchers‎ in different abstract spaces‎. In this paper‎, ‎we consider best coapproximation by closed unit balls‎. ‎We define qcoproximinal and coremotal‎, ‎and find some theorems. پرونده مقاله

w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces پرونده مقاله