@article{Shahzad2026, 
author = {Naseer Shahzad and Amer Hassan Albargi and Manahell Alsosui},
title = {g-Averaged Halpern-type convergence theorems for enriched    g-nonexpansive mappings in Hilbert spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13023-13041},
keywords = {fixed point, attractive point, enriched g-nonexpansive mapping, metric projection, Halpern-type iteration, averaged g-mapping},
url = {https://www.sciopen.com/article/10.3934/math.2026536},
doi = {10.3934/math.2026536},
abstract = {We introduce the set of    g-attractive points of a mapping    f and study a    g-averaged Halpern-type iterative scheme for    b-enriched    g-nonexpansive mappings in real Hilbert spaces. For    0  <    λ  ≤    1      /    (  b  +  1  ), we prove that every sequence generated by the scheme converges strongly-after applying    g-to the metric projection of the anchor onto the set        A          g        (      f          g      ,      λ        ), provided this set is nonempty. As a consequence, we obtain the corresponding strong convergence theorem for    b-enriched nonexpansive mappings. A numerical example is given to illustrate the method and the role of the averaging parameter.}
}