Modified hybrid algorithms for Lipschitz quasi-pseudo-contractive mappings in Hilbert spaces

In this paper, strong convergence theorems are obtained by modified hybrid methods for Lipschitz quasi-pseudo-contractions in a Hilbert space. Besides, applications of these theorems are introduced. Finally, we use these methods to modify Ishikawaʹs iteration process and get some strong convergence theorems which are different from Zhou [H.Y. Zhou, Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 343 (2008) 546 556].