Let X be a linear space, and \(x, y \in X\). The x, y joining x and y is defined x, y = \(\{\lambda x + (1- \lambda)y: 0 \leq \lambda \leq 1\}\). Posted on:
Let \(1 \leq p \leq + \infty\) . If for arbitrary \(x = \{x_k\}, y = \{y_k\} in \(l_p\) and \(\lambda \in K\), define vector addition and scalar multiplication componentwise then \(l_p\) is a \(\hspace{1.0cm}\) space. Posted on:
A nonempty subset C of the vector space X is convex if and only if C contains all \(\hspace{1.0cm}\) of all its elements. Posted on:
Any linear subspace M of \(R^n\) is a convex set since linear subspaces are \(\hspace{1.0cm}\) under addition and scalar multiplication. Posted on:
If \(x^*\in R^n\) and if \(r>0\), then the \(\hspace{1.0cm}\) expressed as \(B(x^*, r) = \{y \in R^n: \textbf{K} y – x^* \textbf{K} Posted on:
If \(f : X \mapsto R\) be a linear functional defined on a linear space X, then f is a \(\hspace{1.0cm}\) function. Posted on:
if A is nonempty subset of a linear space, then the \(\hspace{1.0cm}\) of all convex sets containing A gives you the convex hull of A denoted by co A. Posted on:
Let \(\textbf{K} \cdot \textbf{K}_1\) and \(\textbf{K} \cdot \textbf{K}_2\) be two norms defined on a linear space X. \(\textbf{K} \cdot \textbf{K}_1\) and \(\textbf{K} \cdot \textbf{K}_2\) are equivalent if there exists constants \(a, b > 0\) such that \(\hspace{1.0cm}\) for all \(x \in X\). Posted on:
