Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras

Wuttichai Suriyacharoen; Wutiphol Sintunavarat

doi:10.33205/cma.1715909

Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras

Abstract

Let B be a Banach algebra, and let Ccb(B) denote the set of all closed convex bounded subsets of B. Assume that ⪰ is a partial order defined on Ccb(B), and define D := {A ∈ Ccb(B) : A ≻ 0}, where 0 denotes the zero element of Ccb(B). Furthermore, suppose that for every A,B ∈ D, the set A ⊗ B also belongs to D, where A ⊗ B means the closure of the product set AB. In this paper, general solutions F : D → D of the multiplicative set-valued functional equation F(X ⊗ Y ) = F(X) ⊗ F(Y ) for all X, Y ∈ D are determined. These solutions are closely involved with some set-valued mappings. Moreover, its stability is also proved on Banach algebras. The results not only generalize classical findings in functional equations but also open avenues for further exploration in nonlinear analysis and set-valued operator theory.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Wuttichai Suriyacharoen This is me
0009-0001-3945-729X
Thailand

Wutiphol Sintunavarat ^*
0000-0002-0932-1332
Thailand

Early Pub Date

December 9, 2025

Publication Date

December 15, 2025

Submission Date

June 9, 2025

Acceptance Date

November 27, 2025

Published in Issue

Year 2025 Volume: 8 Number: 4

DOI

https://doi.org/10.33205/cma.1715909

IZ

https://izlik.org/JA85ZA23JY

Cite

RIS / Bibtex

APA

Suriyacharoen, W., & Sintunavarat, W. (2025). Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras. Constructive Mathematical Analysis, 8(4), 187-199. https://doi.org/10.33205/cma.1715909

AMA

1.Suriyacharoen W, Sintunavarat W. Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras. CMA. 2025;8(4):187-199. doi:10.33205/cma.1715909

Chicago

Suriyacharoen, Wuttichai, and Wutiphol Sintunavarat. 2025. “Multiplicative Set--Valued Equation Related to Certain Set--Valued Mappings and Its Stability on Banach Algebras”. Constructive Mathematical Analysis 8 (4): 187-99. https://doi.org/10.33205/cma.1715909.

EndNote

Suriyacharoen W, Sintunavarat W (December 1, 2025) Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras. Constructive Mathematical Analysis 8 4 187–199.

IEEE

[1]W. Suriyacharoen and W. Sintunavarat, “Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras”, CMA, vol. 8, no. 4, pp. 187–199, Dec. 2025, doi: 10.33205/cma.1715909.

ISNAD

Suriyacharoen, Wuttichai - Sintunavarat, Wutiphol. “Multiplicative Set--Valued Equation Related to Certain Set--Valued Mappings and Its Stability on Banach Algebras”. Constructive Mathematical Analysis 8/4 (December 1, 2025): 187-199. https://doi.org/10.33205/cma.1715909.

JAMA

1.Suriyacharoen W, Sintunavarat W. Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras. CMA. 2025;8:187–199.

MLA

Suriyacharoen, Wuttichai, and Wutiphol Sintunavarat. “Multiplicative Set--Valued Equation Related to Certain Set--Valued Mappings and Its Stability on Banach Algebras”. Constructive Mathematical Analysis, vol. 8, no. 4, Dec. 2025, pp. 187-99, doi:10.33205/cma.1715909.

Vancouver

1.Wuttichai Suriyacharoen, Wutiphol Sintunavarat. Multiplicative set--valued equation related to certain set--valued mappings and its stability on Banach algebras. CMA. 2025 Dec. 1;8(4):187-99. doi:10.33205/cma.1715909