Approximating Fixed Points of a General Class of Nonexpansive Mappings in Banach Spaces with Applications

Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces

“…Since then, a number of generalizations and extensions of nonexpansive mappings and their results have been obtained by many authors. Some of the notable extensions and generalizations of nonexpansive mappings can be found in [4][5][6][7][8][9][10][11][12][13][14] and elsewhere.…”

“…Pant and Shukla [13] combined the SGNM with Aoyama and Kohsaka [4] type α-nonexpansive mappings and introduced the notion of generalized α-nonexpansive mappings. Pandey et al [12] combined the SGNM with other type of nonexpansive mappings and introduced a new class of mappings called α-Reich-Suzuki nonexpansive mappings. They also showed that the class of α-Reich-Suzuki nonexpansive mappings is contained in the class of mappings satisfying condition (E).…”

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

“…Soon, Iqbal et al [13] showed that their idea holds for the case of multivalued mappings. In 2019, Pandey et al [14] introduced the notion of β-Riech-Suzuki type nonexpansive selfmaps. Recently, Maldar et al [15] obtained the multi-valued version of these maps.…”

“…In 2020, Ullah et al [16] defined generalized (α, β)-nonexpansive maps. These maps are very important because they included both of the classes due to Pant and Shukla [12] and Pandey et al [14]. The purpose of the present work is to provide the multi-valued version of these maps and to study the related fixed point results.…”

Iterative Approximations for a Class of Generalized Nonexpansive Operators in Banach Spaces

“…Garcia-Falset et al [5] proved that every Suzuki mapping satisfies condition (E) with μ � 3. Notice also that the class of Garcia-Falset mappings also includes many other classes of generalized nonexpansive (see [6] for details). In this paper, we study in deep this general class of mapping.…”