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The semiclassical corrections to the Cardy-Verlinde entropy of a five-dimensional Schwarzschild anti de-Sitter black hole ($SAdS_{5}$) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitation effect. In addition, a four-dimensional timelike brane is considered as the boundary of the $SAdS_{5}$ bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. Exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis, can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of $SAdS_{5}$ bulk black hole as the source for stiff matter. A very interesting feature of the solutions of FRW equation is that they all (for $k=0,\pm1$) have a non-vanishing minimum value for the scale factor.
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