Abstract
As an alternative to classical calculus, Grossman and Katz (Non-Newtonian Calculus, 1972) introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus etc. Following Grossman and Katz, we construct the field R(N) of non-Newtonian real numbers and the concept of non-Newtonian metric. Also, we give the triangle and Minkowski's inequalities in the sense of non-Newtonian calculus. Later, we respectively define the sets (N), (N), c(N), c 0 (N) and p (N) of all, bounded, convergent, null and p-absolutely summable sequences in the sense of non-Newtonian calculus and show that each of the sets forms a vector space on the field R(N) and a complete metric space.
Keywords
Mathematics
Calculus (dental)
Minkowski space
Pure mathematics
Metric space
Limit of a sequence
Bounded function
Mathematical analysis
Geometry
Limit (mathematics)
Subject Areas
Approximation Theory and Sequence Spaces
·Statistics and Probability ·Physical Sciences
Fixed Point Theorems Analysis
·Geometry and Topology ·Physical Sciences
Advanced Banach Space Theory
·Mathematical Physics ·Physical Sciences
Citations by Year
2013: 1
2014: 3
2015: 4
2016: 6
2017: 6
2018: 4
2019: 5
2020: 4
2021: 9
2022: 5
2023: 13
2024: 11
2025: 7
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