Another fixed point theorem for nonexpansive potential operators

作者：Ricceri Biagio^*

来源：Studia Mathematica, 2012, 211(2): 147-151.

DOI：10.4064/sm211-2-3

• fixed point
• nonexpansive potential operator
• Jensen inequality

We prove the following result: Let X be a real Hilbert space and let J : X -%26gt; R be a C-1 functional with a nonexpansive derivative. Then, for each r %26gt; 0, the following alternative holds: either J%26apos; has a fixed point with norm less than r, or %26lt;br%26gt;sup(vertical bar vertical bar x vertical bar vertical bar=r) J(x)= sup(vertical bar vertical bar u vertical bar vertical bar L2([0, 1], x)=r) integral(1)(0) J(u(t))dt.

• 出版日期2012