Using an extrapolation procedure proposed by one of us, whichn is based on rigorous properties of Padé approximants, we compute forward Kp dispersion relations. Among other results. we get averages of the absorptive part of the amplitude in the unphysical cut, and the absolute bounds , and statistical estimate and errors , for the combination . This is to be compared with the result of the polynominal extrapolation of Cutkosky and Deo, , the lower bound of Rogers, /4gp >/ 10, and a host of model - dependent calculations for which ranges between 4 and 20.