The Wild Thornberrys Games Wildlife

between the fixed point theorem of Banach and Kannan (modular)

The following result provides a modular version of a synthesis between

fixed point theorems of Banach and

Kannan (see 9/10/2006 post).

Theorem.

Let rho} {E_ complete modular space, or mdulaire

rho satisfies the condition delta2. D is a subset

rho-rho E_ {farm}. T is an application (not necessarily

rho-continuous) from D to D satisfying:

There are two constants c> 1 and k in ( 0.1) as

rho (c (Tx-Ty)) <=liminf rho(x(n)-Tx(n))=a.

Then T admits a fixed point. <= rho(Tz-T^{2}z)< rho(z-Tz)<=a;