본문 바로가기
KERD
논문KCI 등재

Orthogonal Stability of an Euler-­Lagrange-­Jensen (a, b)-­cubic Functional Equation

JOHN MICHAEL RASSIAS|이정례|심은화|NARASIMMAN PASUPATHI
한국수학교육학회|2022.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제29권 제2호|pp. 189-199|DOI https://doi.org/10.7468/jksmeb.2022.29.2.189

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Hyers-Ulam stabilityEuler-Lagrange-Jensen cubic functional equationorthogonality normed space
주제분류수학

초록

In this paper, we introduce a new generalized (a,b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

Abstract

In this paper, we introduce a new generalized (a,b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

참고문헌 (20)

  1. I. Chang, "Nearly general septic functional equation", J. Funct. Spaces, 2021 (2021)
  2. Y. Ding, "Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces", J. Inequal. Appl, 2019 (2019)
  3. F. Drljevic, "On a functional which is quadratic on A-orthogonal vectors", Publ. Inst. Math. (Beograd), 54, pp.63~71 (1986)
  4. M. Fochi, "Functional equations in A-orthogonal vectors", Aequationes Math, 38, pp.28~40 (1989)
  5. P. Găvruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
  6. R. Ger, "Stability of the orthogonal additivity", Bull. Polish Acad. Sci. Math, 43, pp.143~151 (1995)
  7. V. Govindan, "Solution of a 3-D cubic functional equation and its stability", AIMS Math, 5, pp.1693~1705 (2020)
  8. D.H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci, 27, pp.222~224 (1941)
  9. K. Jun, "On the stability of Euler-Lagrange type cubic mappings in quasiBanach spaces", J. Math. Anal. Appl, 332, pp.1335~1350 (2007)
  10. S. Jung, "On the stability of the linear functional equation in a single variable on complete metric spaces", J. Global Optim, 59, pp.13~16 (2014)
  11. Y. Lee, "Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation", J. Math. Inequal, 12, pp.43~61 (2018)
  12. C. Park, "Two multi-cubic functional equations and some results on the stability in modular spaces", J. Inequal. Appl, 2020 (2020)
  13. J. M. Rassias, "On approximately of approximately linear mappings by linear mappings", J. Funct. Anal, 46, pp.126~130 (1982)
  14. J. M. Rassias, "On the stability of the Euler-Lagrange functional equation", Chinese J. Math, 20, pp.185~190 (1992)
  15. J. M. Rassias, "Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings", J. Math. Anal. Appl, 220, pp.613~639 (1998)
  16. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Am. Math. Soc, 72, pp.297~300 (1978)
  17. K. Ravi, "On the Ulam stability for the orthogonally general Euler-Lagrange type functional equation", Int. J. Math. Sci, 3(8), pp.36~47 (2008)
  18. G. Szabo, "Sesquilinear-orthogonally quadratic mappings", Aequationes Math, 40, pp.190~200 (1990)
  19. K. Tamilvanan, "General solution and satbility of additive-quadratic functional equation in IRN-space", J. Funct. Spaces, 2021 (2021)
  20. S.M. Ulam, "A Colloection of the Mathematical Problems" (1960), Interscience Publ

관련 논문AI추천

A Fixed Point Approach to the Orthogonal Stability of Mixed Type Functional Equations김창일, 전영주영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호Functional equations in orthogonality spaces박춘길, 신동윤강원경기수학회 · 한국수학논문집2012 · 제20권 제1호Generalized Hyers-Ulam Stability of Some Cubic-quadratic-additive Type Functional EquationsSoon-Mo Jung, Yang-Hi Lee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제1호Orthogonally additive and orthogonally quadratic functional equation박춘길, 이성진, 이정례강원경기수학회 · 한국수학논문집2013 · 제21권 제1호Solution and stability of a functional equation deriving from additive, quadratic and quartic in quasi-Banach spaces박춘길, Mohammad Golestani, Norouz Ghobadipour강원경기수학회 · 한국수학논문집2025 · 제33권 제4호On the Stability of a General Quadratic-Cubic Functional Equation in Non-Archimedean Normed Spaces이양희영남수학회 · East Asian Mathematical Journal2019 · 제35권 제3호

이 간행물의 다른 논문 (6건)

Generalized relative order (α,β) based some growth analysis of composite entire functionsChinmay Biswas, Tanmay Biswaspp. 125-139Modeling Political and Economic Relations between Norway and Russia: A Behavioral Game Theory ApproachMadjid Eshaghi Gordji, Samereh Babaeipp. 141-160Alpha Invariant along Curves for General Polarizations of Del Pezzo Surfaces of Degree 2원준영pp. 161-170A note on two known sums involving central binomial coefficients with an applicationArjun Kumar Rathie, 임동규pp. 171-177Stability of 𝑠-­variable Additive and 𝑙-­variable Quadratic Functional EquationsVediyappan Govindan, Sandra Pinelas, 이정례pp. 179-188
원문 보기