Let \((X,d_x)\) and \((Y,d_Y)\) be arbitrary metric spaces. A mapping \(f:(X,d_x)\rightarrow (Y,d_Y)\) is called a strict contraction if Posted on:
let \(f:\mathbb{R}\rightarrow\mathbb{R}\) be defined by \(f(x)=\left{\begin{array}{rcl} x^2+1,&\mbox{if}&x\leq 0\\\frac{1}{2}(x+2),&\mbox{if}&x\geq 0\end{array}\right\), then \(f\) is Posted on:
If \((E,d)\)is metric space and \(x_0\in E\), then the open ball centred at \(x_0\) of radius \(r>0\) is given by the set Posted on:
Let \((E,d)\) be a metric space and \(K\) a subset of \(E\). Then \(K\) is said to be connected if Posted on:
The Holder’s inequality states that: if \(1\leq p,q<\infty,\frac{1}{q}+\frac{1}{q}=1\) and if \(x_k,y_k,k=1,2,cdots,n\) are complex numnbers then Posted on:
A sequence \({x_n}_{n=1}^{\infty}\) of points in a metric space \((E,d)\) is a Cauchy sequence if Posted on:
Let \((X,d_x)\) and \((Y,d_Y)\) be metric space and let \(f:D(f)\subset X\rightarrow Y\) where \(D(f)\) is the domain of \(f\), then \(f\) is continuous if Posted on:
