@article{Shi2026, 
author = {Jie Shi},
title = {A fixed-point theorem for generalized strictly nonexpansive mappings on bounded sets in complete metric spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {7143-7154},
keywords = {fixed point, nonstandard analysis, generalized strictly nonexpansive mappings},
url = {https://www.sciopen.com/article/10.3934/math.2026294},
doi = {10.3934/math.2026294},
abstract = {This paper offers substantial advances in the theory of fixed points for generalized strictly nonexpansive mappings. We develop a novel proof technique based on nonstandard analysis to establish a new fixed-point theorem. The core result demonstrates that, in a complete metric space, every continuous generalized strictly nonexpansive mapping with a bounded orbit possesses a unique fixed point to which all iterative sequences converge. The significance of this theorem lies in its substantial relaxation of the classical framework: It entirely dispenses with compactness and convexity requirements, which are typically indispensable in the study of nonexpansive mappings (such as in the Browder–Göhde theorem), replacing them solely with a boundedness condition.}
}