Approximate multi-Jensen-cubic mappings and a fixed point theorem
Abstract
Keywords
Mathematics Subject Classification (2010)
References
Aoki, Tosio. "On the stability of the linear transformation in Banach spaces." J. Math. Soc. Japan 2 (1950): 64-66.
Bahyrycz, Anna, and Jolanta Olko. "On stability and hyperstability of an equation characterizing multi-Cauchy-Jensen mappings." Results Math. 73, no. 2 (2018): Article 55.
Bahyrycz, Anna, and Krzysztof Cieplinski, and Jolanta Olko. "On an equation characterizing multi-Cauchy-Jensen mappings and its Hyers-Ulam stability." Acta Math. Sci. Ser. B (Engl. Ed.) 35, no. 6 (2015): 1349-1358.
Bahyrycz, Anna, and Krzysztof Cieplinski, and Jolanta Olko. "On an equation characterizing multi-additive-quadratic mappings and its Hyers-Ulam stability." Appl. Math. Comput. 265 (2015): 448-455.
Bodaghi, Abasalt. "Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations." J. Intel. Fuzzy Syst. 30, no. 4 (2016): 2309-2317.
Bodaghi, Abasalt. "Ulam stability of a cubic functional equation in various spaces." Mathematica 55(78), no. 2 (2013): 125-141.
Bodaghi, Abasalt. "Cubic derivations on Banach algebras." Acta Math. Vietnam. 38, no. 4 (2013): 517-528.
Bodaghi, Abasalt, and Seyed Mohsen Moosavi, and Hamidreza Rahimi. "The generalized cubic functional equation and the stability of cubic Jordan *-derivations." Ann. Univ. Ferrara Sez. VII Sci. Mat. 59, no. 2 (2013): 235-250.
Bodaghi, Abasalt, and Choonkil Park, and Oluwatosin Temitope Mewomo. "Multiquartic functional equations." Adv. Difference Equ. 2019: Paper No. 312 (2019).
Bodaghi, Abasalt, and Behrouz Shojaee. "On an equation characterizing multicubic mappings and its stability and hyperstability." Fixed Point Theory to appear.
Brillouët-Belluot, Nicole, and Janusz Brzdek, and Krzysztof Cieplinski. "On some recent developments in Ulam’s type stability." Abstr. Appl. Anal. 2012 (2012): Article ID 71693.
Brzdek, Janusz, and Jacek Chudziak, and Zsolt Páles. "A fixed point approach to stability of functional equations." Nonlinear Anal. 74, no. 17 (2011): 6728-6732.
Brzdek, Janusz, and Krzysztof Cieplinski. "Hyperstability and superstability." Abstr. Appl. Anal. 2013 (2013): Article ID 401756.
Brzdek, Janusz, and Dorian Popa, and Bing Xu. "Remarks on stability of linear recurrence of higher order." Appl. Math. Lett. 23, no. 12 (2010): 1459-1463.
Brzdek, Janusz, and Paweł Wójcik. "On approximate solutions of some difference equations." Bull. Aust. Math. Soc. 95, no. 3 (2017): 476-481.
Cadariu, Liviu I., and Viorel Radu. "Fixed points and the stability of quadratic functional equations." An. Univ. Timisoara Ser. Mat.-Inform. 41, no. 1 (2003): 25-48.
Cieplinski, Krzysztof. "On the generalized Hyers-Ulam stability of multi-quadratic mappings." Comput. Math. Appl. 62, no. 9 (2011): 3418-3426.
Cieplinski, Krzysztof. "Stability of the multi-Jensen equation." J. Math. Anal. Appl. 363, no. 1 (2010): 249-254.
Cieplinski, Krzysztof. "On multi-Jensen functions and Jensen difference." Bull. Korean Math. Soc. 45, no. 4 (2008): 729-737.
Cieplinski, Krzysztof. "Generalized stability of multi-additive mappings." Appl. Math. Lett. 23, no. 10 (2010): 1291-1294.
Gavruta, Pascu. "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings." J. Math. Anal. Appl. 184, no. 3 (1994): 431-436.
Hyers, Donald H. "On the stability of the linear functional equation." Proc. Nat. Acad. Sci. U.S.A. 27 (1941): 222-224.
Jun, Kil-Woung, and Hark Kim. "On the Hyers-Ulam-Rassias stability of a general cubic functional equation." Math. Inequal. Appl. 6, no. 2 (2003): 289-302.
Jun, Kil-Woung, and Hark Kim. "The generalized Hyers-Ulam-Rassias stability of a cubic functional equation." J. Math. Anal. Appl. 274, no. 2 (2002): 267-278.
Jung, Soon-Mo. "Hyers-Ulam-Rassias stability of Jensen’s equation and its application." Proc. Amer. Math. Soc. 126, no. 11 (1998): 3137-3143.
Jung, Soon-Mo, and Dorian Popa, and Themistocles M. Rassias. "On the stability of the linear functional equation in a single variable on complete metric groups." J. Global Optim. 59, no. 1 (2014): 165-171.
Kominek, Zygfryd. "On a local stability of the Jensen functional equation." Demonstratio Math. 22, no. 2 (1989): 499-507.
Kuczma, Marek. An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality. Basel: Birkhäuser Basel, 2009.
Lee, Yang-Hi, and Kil Jun. "A generalization of the Hyers-Ulam-Rassias stability of Jensen’s equation." J. Math. Anal. Appl. 238, no. 1 (1999): 305-315.
Park, Choonkil, and Abasalt Bodaghi. "Two multi-cubic functional equations and some results on the stability in modular spaces." J. Inequal. Appl. 2020, Paper No. 6 (2020).
Popa, Dorian. "Hyers-Ulam-Rassias stability of the general linear equation." Nonlinear Funct. Anal. Appl. 7, no. 4 (2002): 581-588.
Popa, Dorian. "Hyers-Ulam-Rassias stability of a linear recurrence." J. Math. Anal. Appl. 309, no. 2 (2005): 591-597.
Prager, Wolfgang, and Jens Schwaiger. "Multi-affine and multi-Jensen functions and their connection with generalized polynomials." Aequationes Math. 69, no. 1-2 (2005): 41-57.
Prager, Wolfgang, and Jens Schwaiger. "Stability of the multi-Jensen equation." Bull. Korean Math. Soc. 45, no. 1 (2008): 133-142.
Rassias, John Michael. "Solution of the Ulam stability problem for cubic mappings." Glas. Mat. Ser. III 36, no. 1 (2001): 63-72.
Rassias, Themistocles M. "On the stability of the linear mapping in Banach spaces." Proc. Amer. Math. Soc. 72, no. 2 (1978): 297-300.
Salimi, Somaye, and Abasalt Bodaghi. "A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings." J. Fixed Point Theory Appl. 22, no. 1 (2020): Article No. 9.
Ulam, Stanisław. Problems in Modern Mathematics, New York: John Wiley and Sons, 1940.
Xu, Tian Zhou. "Stability of multi-Jensen mappings in non-Archimedean normed spaces." J. Math. Phys. 53, no. 2 (2012): Article No. 023507.
Zhao, Xiaopeng, and Xiuzhong Yang, and Chin Pang. "Solution and stability of the multiquadratic functional equation." Abstr. Appl. Anal. 2013 (2013): Article ID 415053. Cited on 142.
Download statistics: 500
This article by Elahe Ramzanpour, Abasalt Bodaghi is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.
Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more
The Journal is indexed in:
AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019