Top

Published in:

2022 | OriginalPaper | Chapter

Approximate Generalized Jensen Mappings in 2-Banach Spaces

Authors : Muaadh Almahalebi, Themistocles M. Rassias, Sadeq Al-Ali, Mustapha E. Hryrou

Published in: Approximation and Computation in Science and Engineering

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Our aim is to investigate the generalized Hyers-Ulam-Rassias stability for the following general Jensen functional equation:

$$\displaystyle \sum _{k=0}^{n-1} f(x+ b_{k}y)=nf(x), $$

where $n \in \mathbb {N}_{2}$, $b_{k}=\exp (\frac {2i\pi k}{n})$ for 0 ≤ k ≤ n − 1, in 2-Banach spaces by using a new version of Brzdȩk’s fixed point theorem. In addition, we prove some hyperstability results for the considered equation and the general inhomogeneous Jensen equation

$$\displaystyle \sum _{k=0}^{n-1} f(x+ b_{k}y)=nf(x)+G(x,y). $$

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Rearrangements, L-Superadditivity and Jensen-Type Inequalities

next chapter The Asymptotic Expansion for a Class of Convergent Sequences Defined by Integrals

M. Almahalebi, A. Chahbi, Approximate solution of p-radical functional equation in 2-Banach spaces. Acta Math. Sci. 39(2), 551–566 (2019)MathSciNetCrossRefMATH

T. Aoki, On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2, 64–66 (1950)MathSciNetCrossRefMATH

J.A. Baker, A general functional equation and its stability. Proc. Am. Math. Soc. 133, 1657–1664 (2005)MathSciNetCrossRefMATH

J. Brzdȩk, Stability of additivity and fixed point methods. Fixed Point Theory Appl. 2013, 265 (2013)

J. Brzdȩk, K. Ciepliński, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces. Nonlinear Anal. 74, 6861–6867 (2011)

J. Brzdȩk, K. Ciepliński, On a fixed point theorem in 2-Banach spaces and some of its applications. Acta Math. Sci. 38(2), 377–744 (2018)

J. Brzdȩk, E. Karapinar, A. Petruşel, A fixed point theorem and the Ulam stability in generalized dq-metric spaces. J. Math. Anal. Appl. 467(1), 501–520 (2018)

A. Chahbi, M. Almahalebi, A. Charifi, S. Kabbaj, Generalized Jensen functional equation on restricted domain. Ann. West Univ. Timisoara-Math. 52, 29–39 (2014)MathSciNetMATH

A.B. Chahbi, A. Charifi, B. Bouikhalene, S. Kabbaj, Non-archimedean stability of a Pexider K-quadratic functional equation. Arab J. Math. Sci. 21, 67–83 (2015)MathSciNetMATH

10.

S. Gähler, 2-metrische Räume und ihre topologische Struktur. Math. Nachr. 26, 115–148 (1963)MathSciNetCrossRefMATH

11.

S. Gähler, Linear 2-normiete Räumen. Math. Nachr. 28, 1–43 (1964)MathSciNetCrossRef

12.

P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)MathSciNetCrossRefMATH

13.

D.H. Hyers, On the stability of the linear functional equation. Proc. Nat. Acad. Sci. USA 27, 222–224 (1941)MathSciNetCrossRefMATH

14.

R. Łukasik, Some generalization of Cauchy’s and the quadratic functional equations. Aequat. Math. 83, 75–86 (2012)MathSciNetCrossRefMATH

15.

W.-G. Park, Approximate additive mappings in 2-Banach spaces and related topics. J. Math. Anal. Appl. 376, 193–202 (2011)MathSciNetCrossRefMATH

16.

T.M. Rassias, On the stability of linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)MathSciNetCrossRefMATH

17.

H. Stetkær, Functional equations involving means of functions on the complex plane. Aequat. Math. 55, 47–62 (1998)MathSciNetCrossRefMATH

18.

S.M. Ulam, Problems in Modern Mathematics (Wiley, New York, 1960)MATH

Title: Approximate Generalized Jensen Mappings in 2-Banach Spaces
Authors: Muaadh Almahalebi
Themistocles M. Rassias
Sadeq Al-Ali
Mustapha E. Hryrou
Publisher: Springer International Publishing
Book: Approximation and Computation in Science and Engineering
Print ISBN: 978-3-030-84121-8

Electronic ISBN: 978-3-030-84122-5

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-3-030-84122-5_2

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner