A New Fixed-Point Framework for Nonexpansive and Averaged Mappings in Normed GE-Algebras

Prashant Patel, Ravikumar Bandaru and Amal S. Alali

Journal of Mathematics, 2026, vol. 2026, 1-14

Abstract: In this paper, we develop a systematic framework for studying fixed-point theory in the setting of normed GE-algebras. Building on the GE-norm, we introduce and analyze nonexpansive mappings, α-averaged mappings, and enriched contractions with respect to the quasimetric induced by the GE-norm. Several new fixed point results are established, including the nonexpansiveness of averaged operators, a demiclosedness principle, and the sequential closedness of fixed-point sets. We further prove convergence theorems for Picard-type iterations associated with α-averaged and enriched nonexpansive mappings, thereby extending classical fixed point principles from normed linear and metric spaces to the broader, nonsymmetric, and algebraic setting of GE-algebras. The results presented here demonstrate that normed GE-algebras provide a natural and robust framework for nonlinear operator theory and open new directions for fixed point analysis within algebraic systems.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/7377821.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/7377821.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7377821

DOI: 10.1155/jom/7377821

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().