Iterative approximation of common attractive points of further generalized hybrid mappings

Abstract

Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl. 2013:69, 2013, https://doi.org/10.1186/1687-1812-2013-69) generalized to the case of two mappings in Hilbert spaces without closedness assumption. Our results are generalizations and improvements of several results in the literature in different ways.