Rubio de Francia extrapolation theorem in variable Lebesgue spaces for B_p(?) weights

In this paper, we prove Rubio de Francia extrapolation results for pair of non-increasing functions with Bp((center dot)) weights. The case of B-infinity weights has also been proved. These results have been applied to obtain the extrapolation results in the framework of variable exponent Lebesgue space L-w(p(center dot)) with Luxemburg norm. Also, an improved norm estimate for the boundedness of Hardy averaging operator on variable exponent Lebesgue space is given.