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

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

—>> there exist a constant \(k\in[0,1)\) such that \(d_Y(f(x),f(y))\leq kd_X(x,y)\) for all \(x,y\in X\)

there exist a constant \(k\in[0,1)\) such that \(d_Y(x,y)\leq kd_Y(x,y)\) for all \(x,y\in X\)

there exist a variable \(k\in\mathbb{N}\) such that \(d_X(f(x),f(y))\geq kd(x,y)\) for all \(x,y\in X\)

there exist a constant \(k\in\mathbb{N})\) such that \(d_Y(x,y)geq kd_X(x,y)\) for all \(x,y\in X\)

Leave a Reply

MEET OVER 2000 NOUN STUDENTS HERE. 

Join us for latest NOUN UPDATES and Free TMA answers posted by students on our Telegram. 

OUR ONLINE TUTORIAL CLASS IS NOW ON!!! JOIN US NOW. 
JOIN NOW!
close-link