K-uniform convexity in Orlicz-Lorentz function space equipped with the Orlicz norm

The necessary and sufficient conditions for k-uniform convexity in Orlicz-Lorentz function spaces equipped with the Orlicz norm and generated by N-functions as well as any non-increasing weight sequences are given. Moreover, Some tools useful in the proofs of the main results are also provided. Besides, in the proof process, we use the reachability of the infimum in Orlicz norm formula to obtain a function working like supporting functional, which makes us complete the proof even though the characterization of dual space is still unclear.