참고문헌
- J. Appell and P. P. Zabrejko, Nonlinear Superposition Operator, Cambridge University Press, New York, 1990.
- V. V. Chistyakov, Mappings of generalized variation and composition operators, J. Math. Sci. (New York) 110 (2002), no. 2, 2455-2466. https://doi.org/10.1023/A:1015018310969
-
J. A. Guerrero, H. Leiva, J. Matkowski, and N. Merentes, Uniformly continuous composition operators in the space of bounded
${\phi}$ -variation functions, Nonlinear Anal. 72 (2010), no. 6, 3119-3123. https://doi.org/10.1016/j.na.2009.11.051 - M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Editors and Silesian University, Warszawa-Krakow-Katowice, 1985.
- K. Lichawski, J. Matkowski, and J. Mis, Locally defined operators in the space of differentiable functions, Bull. Polish Acad. Sci. Math. 37 (1989), no. 1-6, 315-325.
- W. A. Luxemburg, Banach Function Spaces, Ph.D. thesis, Technische Hogeschool te Delft, Netherlands, 1955.
- L. Maligranda and W. Orlicz, On some properties of functions of generalized variation, Monatsh. Math. 104 (1987), no. 1, 53-65. https://doi.org/10.1007/BF01540525
- J. Matkowski, Functional equations and Nemytskii operators, Funkcial. Ekvac. 25 (1982), no. 2 127-132.
- J. Matkowski, Uniformly bounded composition operators between general Lipschitz function normed spaces, Topol. Methods Nonlinear Anal. 38 (2011), no. 2, 395-406.
- J. Matkowski, Uniformly continuous superposition operators in the spaces of bounded variation functions, Math. Nachr. 283 (2010), no. 7, 1060-1064.
- J. Matkowski and J. Mis, On a characterization of Lipschitzian operators of substitution in the space BV (a, b), Math. Nachr. 117 (1984), 155-159. https://doi.org/10.1002/mana.3211170111
- J. Musielak and W. Orlicz, On generalized variations. I, Studia Math. 18 (1959), 11-41. https://doi.org/10.4064/sm-18-1-11-41
- H. Nakano, Modulared Semi-Ordered Linear Spaces, Tokyo, 1950.
- W. Orlicz, A note on modular spaces. I, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 9 (1961), 157-162.
- N. Wiener, The quadratic variation of function and its Fourier coefficients, Massachusett J. Math. 3 (1924), 72-94.
- M. Wrobel, On functions of bounded n-th variation, Ann. Math. Sil. No. 15 (2001), 79-86.
- M. Wrobel, Lichawski-Matkowski-Mis theorem of locally defined operators for functions of several variables, Ann. Acad. Pedagog. Crac. Studia Math. 7 (2008), 15-22.
- M. Wrobel, Locally defined operators and a partial solution of a conjecture, Nonlinear Anal. 72 (2010), no. 1, 495-506. https://doi.org/10.1016/j.na.2009.06.093
- M. Wrobel, Representation theorem for local operators in the space of continuous and monotone functions, J. Math. Anal. Appl. 372 (2010), no. 1, 45-54. https://doi.org/10.1016/j.jmaa.2010.06.013
- M. Wrobel, Locally defined operators in Holder's spaces, Nonlinear Anal. 74 (2011), no. 1, 317-323. https://doi.org/10.1016/j.na.2010.08.046
- L. C. Young, Sur une generalisation de la notion de variation de puissance p-ieme bornee au sens de N. Wiener, et sur la convergence des series de Fourier, C. R. Acad. Sci. 204 (1937), no. 7, 470-472.
피인용 문헌
- Uniformly Bounded Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz vol.04, pp.04, 2015, https://doi.org/10.4236/ijmnta.2015.44017