Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces

Approximation of Fixed Points of Multivalued Generalized (α,β)-Nonexpansive Mappings in an Ordered CAT(0) Space

“…Through numerical experiments we have shown that the process (6) converges faster than all the leading schemes. The proposed mapping and results generalize and extend various results in CAT(0) space including [20,27,31,40]. Furthermore, we have also presented an application of the results in approximating the solution of integral equations.…”

“…(1) Multivalued generalized (α,β)-nonexpansive mappings extend and generalize the class of mappings introduced by [31]. Indeed, if α = β then the mapping is reduced to multivalued generalized α-nonexpansive mapping.…”

“…The class of α-nonexpansive mappings in Banach spaces were suggested by Aoyama and Kohshaka [30] who also explored fixed points of such mappings. Recently, Iqbal et al [31] proposed the concept of multivalued generalized α-nonexpansive mappings and obtained existence and approximation results in the setting of a Banach space. In 2018, Harandi et al [32] presented the class of (α, β)-nonexpansive mappings which is properly larger than the class of α-nonexpansive mapping for a fixed point sequence.…”

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

“…For finding fixed points of these maps, we have provided the multi-valued version of the M-iteration and showed, by an example, that it is more effective than the other iterative schemes. Since multi-valued (α, β)-nonexpansive are more general than the multi-valued generalized α-nonexpansive and multi-valued Reich-Suzuki type nonexpansive maps, we conclude that our main outcome improves and extends the corresponding results of Iqbal et al [13] and Maldar et al [15].…”

“…In the year 2017, Pant and Shukla [12] studied the class of generalized α-nonexpansive mappings and showed that this new class of maps properly included Suzuki maps [8] and partially included α-nonexpansive maps due to Aoyama and Kohsaka [10]. 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.…”