*Department of Mathematics, University College of Engineering, Panruti, India
**Department of Mathematics, Government College of Engineering, Srirangam, Tiruchirappalli, India
Online published on 2 July, 2016.
Motivated by the theory of valued inner product space, our aim in this paper is to generalize it in t(n) settings. As a consequence we introduce the notion of t(n)-valued norm and t(n)-valued inner product space. We derive general linearly independent vector having the property to yield the even number 2 with the inner product of an orthogonal vector. We extend the same with the existence of a vector that satisfy Pythagorean equation and derive a general formula using Gram-Schmidt process for the function t(n). We conclude the paper with an application of t(n)-valued inner product space in a travelling salesmen problem.
norm, inner product, t(n)-valued norm, t(n)-valued inner product, travelling salesmen
