Fixed point results involving a finite family of enriched strictly pseudocontractive and pseudononspreading mappings

Abstract

In this study, we introduce a method for finding common fixed points of a finite family of $(\eta _{i}, k_{i})$ -enriched strictly pseudocontractive (ESPC) maps and $(\eta _{i}, \beta _{i})$ -enriched strictly pseudononspreading (ESPN) maps in the setting of real Hilbert spaces. Further, we prove the strong convergence theorem of the proposed method under mild conditions on the control parameters. Our main results are also applied in proving strong convergence theorems for $\eta _{i}$ -enriched nonexpansive, strongly inverse monotone, and strictly pseudononspreading maps. Some nontrivial examples are given, and the results obtained extend, improve, and generalize several well-known results in the current literature.