@article{Civgin2025, 
author = {Emre Civgin and Numan Yalcin},
title = {Algebraic and topological foundations of non-Newtonian analysis via generator functions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {26633-26661},
keywords = {alpha generator function, algebraic structures, topological structures, star operators, star vector space},
url = {https://www.sciopen.com/article/10.3934/math.20251171},
doi = {10.3934/math.20251171},
abstract = {In this paper we explored the algebraic and topological underpinnings of non-Newtonian analysis through the framework of a generator function    α. We introduced the    α-number systems and the associated arithmetic operations, and we established the corresponding algebraic structures, including groups, fields, and vector spaces defined over    α-real numbers. On the topological side, we developed the notions of    α-metric spaces and    α-sequences, thereby extending core concepts of analysis to the non-Newtonian setting. The study culminates with the formulation of star (   ⋆) analysis, which provides a systematic mechanism for transitioning between distinct arithmetic systems, together with a rigorous treatment of    ⋆-vector spaces and linear operators.}
}