ABSTRACT
The usual modulus function of a real number is the maximum of the real number and the additive inverse of the real number. The multiplicative modulus function of a positive real number is the maximum of the positive real number and the multiplicative inverse of the positive real number. This is the beginning of the “multiplicative” mathematics. The possibilities for extensions of various branches of mathematics have already been studied for “multiplicative” branches. This article presents a study on possibilities for extensions of functional analysis to multiplicative functional analysis.
References
-
D.E. Alspach, A fixed point free nonexpansive map. Proceedings of the American Mathematical Society 82(3) (1981) 423-424.
-
D. Aniszewska, Multiplicative runge–kutta methods. Nonlinear Dynamics 50(1-2) (2007) 265-272.
-
M. E. Aydin, A. Has, B. Yilmaz, Multiplicative rectifying submanifolds of multiplicative Euclidean space. Mathematical Methods in the Applied Sciences 2024 (2024) 1–11, DOI 10.1002/mma.10329.
-
A.E. Bashirov, E.M. Kurpınar, A. Özyapıcı, Multiplicative calculus and its applications. Journal of Mathematical Analysis and Applications 337(1) (2008) 36-48.
-
N. Castro, M. Reyes, Hausdorff measures and dimension on ℝ∞. Proceedings of the American Mathematical Society 125(11) (1997) 3267-3273.
-
R.O. Davies, A property of Hausdorff measure. Mathematical Proceedings of the Cambridge Philosophical Society 52(1) (1956) 30-34.
-
M.M. Day, Some characterizations of inner-product spaces. Transactions of the American Mathematical Society 62(2) (1947) 320-337.
-
R.E. Edwards, Multiplicative norms on Banach algebras. Mathematical Proceedings of the Cambridge Philosophical Society 47(3) (1951) 473-474.
-
P.H. Enflo, A counterexample to the approximation problem in Banach spaces. Matematika 18(1) (1974) 146-155.
-
L. Ingelstam, Real Banach algebras. Arkiv för matematik 5(3) (1964) 239-270.
-
H. Kizmaz, On certain sequence spaces. Canadian Mathematical Bulletin 24(2) (1981) 169-176.
-
B. Lavrič, Continuity of order-preserving functions. Commentationes Mathematicae Universitatis Carolinae 38(4) (1997) 645-655.
-
S. Loganathan, C.G. Moorthy, A net convergence for Schauder double bases. Asian-European Journal of Mathematics 9(1) (2016) Article Id.1650010.
-
C.G. Moorthy, A problem of Good on Hausdorff dimension. Mathematika 39(2) (1992) 244-246.
-
C.G. Moorthy, Infinite products using multiplicative modulus function. Mathematics Student 88 (2019) 39-54
-
C.G. Moorthy, Applicable multiplicative calculus using multiplicative modulus function. Fundamental Journal of Mathematics and Applications 2(2) (2019) 195-199.
-
C.G. Moorthy, Fixed point formulation using exponential logarithmic transformations and its applications. Fundamental Journal of Mathematics and Applications 3(2) (2020) 125-136.
-
C.G. Moorthy, Singular multiplicative calculus using multiplicative modulus function. Mathematics Student 91 (2022) 19-33.
-
C.G. Moorthy, Points at infinity in topological vector spaces. World Scientific News 192 (2024) 88-100.
-
R.W.K. Odoni, Multiplicative forms and associative algebras. Journal of the London Mathematical Society 2(2) (1974) 198-200.
-
S. Ramkumar, C.G. Moorthy, A construction for topological extensions. Asia-European Journal of Mathematics 4(3) (2011) 481-494.
-
C.A. Rogers, S.J. Taylor, The analysis of additive set functions in Euclidean space. Acta Math.101 (1959) 273–302.
-
G. Siva, C.G. Moorthy, Reviewed techniques in automatic continuity of linear functionals. Khayyam Journal of Mathematics 9(1) (2023) 1-29.
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