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"In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show thatevery Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping.We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and \Delta-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed."

Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs