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Very recently, the notion of graphical rectangular b -metric spaces has been introduced, where the weight of the symmetric edges endowing the directed graph is defined in terms of the underlying metric. Due to its intimate relationship with the directed graphs, such spaces have a wide range of applications in science and engineering. In this paper, we rectify some errors that arose in the paper [Younis et al., A novel approach of graphical rectangular b -metric spaces with an application to the vibrations of a vertical heavy hanging cable, J. Fixed Point Theory Appl. 21(1) (2019) 33]. We show that the main result of the paper described above can be modified, and we present the same in this note. [ABSTRACT FROM AUTHOR]

We study perturbations of a hybrid steepest descent method for locating common fixed points of an arbitrary pool { T λ } of nonexpansive mappings. The difficulty of handling a possibly uncountable family is settled down to dealing with a countable family of auxiliary mappings { S n } associated to { T λ } , in the sense that the approximate fixed points of { S n } provide the common fixed points of { T λ }. Algorithms with strong convergence for solving the associated variational inequality problems are presented. Applications to convex minimization problems and convex feasibility problems are provided, together with numerical examples for comparisons of our algorithms with the existing ones. [ABSTRACT FROM AUTHOR]