Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: https://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2023, 11(1), 7-18
DOI: 10.12691/tjant-11-1-2
Open AccessArticle

Stability Results of the Additive and Quartic Functional Equations in Random p-Normed Spaces

Sushma Devi1, , Asha Rani2, 3 and Manoj Kumar3

1Kanya Mahavidyalaya, Kharkhoda

2Pt. NRS Govt. College, Rohtak

3Baba Mastnath University, AsthalBohar, Rohtak

Pub. Date: May 30, 2023

Cite this paper:
Sushma Devi, Asha Rani and Manoj Kumar. Stability Results of the Additive and Quartic Functional Equations in Random p-Normed Spaces. Turkish Journal of Analysis and Number Theory. 2023; 11(1):7-18. doi: 10.12691/tjant-11-1-2

Abstract

In this paper, we investigate the Hyers-Ulam stability of mixed type additive and quartic functional equations in Random p-normed spaces by direct and fixed-point method.

Keywords:
Hyers-Ulam stability additive functional equation quartic functional equation random p-normed spaces fixed point method direct method

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Ulam S. M., “A collection of the Mathematical Problems”, Interscience Publishers: New York, NY, USA, (1964).
 
[2]  Hyers D.H., “On the stability of the linear functional equation”, Proc. Nat. Acad. Sci. USA, 27, 222-224, 1941.
 
[3]  Aoki T., “On the stability of the linear transformation in Banach spaces”, Journal of the Mathematical Society of Japan, (2) 64-66, 1950.
 
[4]  Rassias J. M., “On approximately of linear mappings by linear mappings”, J. Funct. Anal. USA., 46(1), 126-130, 1982.
 
[5]  Gajda Z., “On stability of additive mappings”, Intern. J. Math. & Math. Sci., 14(3), 431-434, 1991.
 
[6]  Gavruta P.A., “Generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings”, J. Math. Anal. Appl., 184, 431-436, 1994.
 
[7]  Rassias, Th.M., “On the stability of the linear mapping in Banach Spaces”, Proc. Amer. Math. Soc., 72, 297-300, 1978.
 
[8]  Mihet D. and Radu V., “ On the stability of the additive Cauchy functional equation in Random Normed Spaces”, J. Math. Anal. Appl., 343, 567-572 ,2008.
 
[9]  Alessa N., Tamilvanan K., Balasubramanian G. and Loganathan K., “Stability results of the functional equation deriving from quadratic function in Random Normed spaces”, AIMS Mathematics,6(3) 2385-2397, 2021.
 
[10]  Kang M. K., “Random stability of Quadratic Functional Equations”, Journal of Advances in Physics, 16(1), 2019.
 
[11]  Mihet D., Saadati R. and Vaezpour S.M., “The Stability of the Quartic Functional Equation in Random Normed Spaces” Acta Applicandae Mathematicae, 110, 797-803, 2010.
 
[12]  Baktash E., Cho Y.J., Jalili M., Saadati R. and Vaezpour S. M., “On the stability of cubic mappings and quadratic mappings in random normed spaces”, J. Inequalitiesand applications, 2008.
 
[13]  Golet I., “Random p-normed spaces and applications to random functions”, Istanbul Univ. Fen Fak. Mat. Fiz. Astro. Derg, 1, 31-42, 2004-2005.
 
[14]  Sherstnev A. N., “On the notion of a random normed space”, Dokl. Akad. Nauk SSSR, 149, 280-283, 1963.
 
[15]  Schweizer B. and Skla rA., “Probabilistic Metric Spaces”, Elsevier, North Holand, New York, (1983).
 
[16]  Mohiuddine S.A. and Alghamdi M. A, “Stability of Functional equation obtained through a Fixed-point alternative in intuitionstic Fuzzy normed spaces”, Advances in Differences 141, 1-16, August 2012.
 
[17]  Senthil Kumar B. V., Sabarinathan S. and Chandrasekaran A. D., “Stability of a mixed type additive and quartic functional equation”, AIP Conference Proceedings. 2112, 1-7, 2019.
 
[18]  Diaz J. B. and Margolis B., “A fixed point theorem of the alternative for contractions on a generalized complete metric space”, Bull. Amer. Math. Soc., 74 (2), 305-309, March 1968.