This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$

This is the User s Guide to the GTM Toolbox a set of Matlab functions and scripts that implements and demonstrates the generative topographic mapping a method for density modelling dimensionality reduction and data visualisation This document gives a brief description of the GTM the content of the toolbox and what is required to use it It describes how to use the toolbox and provides a section ...

Single crystals of Schiff base compound 2-[(2-chloro-4-nitrophenyl) iminomethyl] phenol (1) were grown by the slow evaporation technique at room temperature. The crystal structure of the title compound was determined by single crystal X-ray diffraction. The title compound crystallizes in the monoclinic system, space group P21, with two symmetry independent molecules. Intramolecular O-H···N hydr...

Nb2O5 nanoparticles were synthesized by the hydrothermal method. Structural, morphological and elemental analysis of synthesized Nb2O5 nanoparticles was carried out using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy, respectively. The average crystal size calculations were performed on the basis ...

Nb2O5 nanoparticles were synthesized by the hydrothermal method. Structural, morphological and elemental analysis of synthesized Nb2O5 nanoparticles was carried out using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy, respectively. The average crystal size calculations were performed on the basis ...

Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...