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n this paper, we introduce the notion of generalized Berinde nonexpansive mappings in metric spaces and show that it is weaker than the notion of Berinde nonexpansive mappings and stronger than the notion of semi-nonexpansive mappings. We also obtain the semiclosed principle, an endpoint theorem, and a common endpoint theorem for generalized Berinde nonexpansive mappings. Strong and Δ-convergence theorems of the Ishikawa iteration process for semi-nonexpansive mappings are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the demiclosed principle, fixed point theorems, and Δ-convergence theorems for the class of generalized hybrid mappings on CAT(κ) spaces with κ > 0. Our results extend the results of Lin et al. (Fixed Point Theory Appl. 2011:49, 2011) and many others. [ABSTRACT FROM AUTHOR]