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To study the four-wave mixing (FWM) effect and wavelength conversion in a hollow core bandgap photonic crystal fiber filled with Ar, we conducted an experiment using a femtosecond laser with the pulse width of 120 fs, a repetition rate of 76 MHz, and tunable central wavelength from 760 to 980 nm. It is observed that new spectra are generated in both sides of the pump at a special wavelength, which can exactly satisfy the phase matching conditions of FWM. Combining experimental results with theoretical analysis, we find that the experimental phenomenon is mainly caused by FWM, and some other nonlinear phase effects, such as self-phase modulation, stimulated Raman scattering, and the soliton effect, have also occurred in this nonlinear process.