Weakly p-Compact, p-Banach-Saks, and Super-reflexive Banach Spaces

New techniques are introduced to extract subsequences satisfying certain upper estimates in suitable Banach spaces. Using these methods, alternative proofs of results of Rakov [Math. Notes26 (1979), 909-916] and Godun and Rakov [Math. Notes31 (1982), 32 39] are obtained. Moreover, these methods provide a useful tool to obtain new examples of Λ-spaces, in the sense of Carne et al. [Trans. Amer. Math. Soc.314 (1989), 639-659].