Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

RASSIAS TH.M.; ELQORACHI E.; Redouani A.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2016 | Volume:7 | Issue:2 Page(s): 279-301

Download Full-Text

View:

213

Download:

Cites:

Information Journal Paper

Title

Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations

Author(s)

RASSIAS TH.M. | ELQORACHI E. | Redouani A. | Issue Writer Certificate

Keywords

semigroup

d'Alembert's equation

Van Vleck's equation

sine function

involution

multiplicative function

homomorphism

superstability

Abstract

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation ∫ Sf(σ (y)xt)dμ (t)− ∫ Sf(xyt)dμ (t)=2f(x)f(y), x, y∈ S, ∫ Sf(σ (y)xt)dμ (t)− ∫ Sf(xyt)dμ (t)=2f(x)f(y), x, y∈ S, where SS is a semigroup, σ σ is an involutive morphism of SS, and μ μ is a complex measure that is linear combinations of Dirac measures (δ zi)i∈ I(δ zi)i∈ I, such that for all i∈ Ii∈ I, zizi is contained in the center of SS. (2) We determine the complex-valued continuous solutions of the following variant of d'Alembert's functional equation ∫ Sf(xty)dυ (t)+∫ Sf(σ (y)tx)dυ (t)=2f(x)f(y), x, y∈ S, ∫ Sf(xty)dυ (t)+∫ Sf(σ (y)tx)dυ (t)=2f(x)f(y), x, y∈ S, where SS is a topological semigroup, σ σ is a continuous involutive automorphism of SS, and υ υ is a complex measure with compact support and which is σ σ-invariant. (3) We prove the superstability theorems of the first functional equation.

Multimedia

No record.

Cites

No record.

References

No record.

Cite

APA: Copy

RASSIAS, TH.M., ELQORACHI, E., & Redouani, A.. (2016). Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 7(2), 279-301. SID. https://sid.ir/paper/340707/en

Vancouver: Copy

RASSIAS TH.M., ELQORACHI E., Redouani A.. Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2016;7(2):279-301. Available from: https://sid.ir/paper/340707/en

IEEE: Copy

TH.M. RASSIAS, E. ELQORACHI, and A. Redouani, “Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 7, no. 2, pp. 279–301, 2016, [Online]. Available: https://sid.ir/paper/340707/en

Related Journal Papers

No record.

Related Seminar Papers

No record.

Related Plans

No record.

Recommended Workshops