Abstract
Recently, Patir et al. [B. Patir, N. Goswami, V.N. Mishra, Some results on fixed point theory for a class of generalized nonexpansive mappings, Fixed Point Theory Appl. (2018)] introduced new class of generalized nonexpansive mappings which is a new condition on mappings called condition B-gamma,B-mu. They studied some existences and convergence theorems for such class of mappings. This new class of mappings is important because it contains the class of Suzuki mappings and hence the class of nonexpansive mappings. In this paper, we further studied this new class of mappings and as a result some new convergence theorems are established using up-to-date iteration process of Hussain et al. [N. Hussain, K. Ullah, M. Arshad, Fixed point approximation of Suzuki generalized nonexpansive mappings via new faster iteration process, J. Nonlinear Convex Anal. 19 (8) (2018) 1383-1393].