Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2026 02 13 Jordan generalized derivation on generalized module extension Banach algebras 10478 10.22075/ijnaa.2025.35693.5308 EN Morteza Essmaili Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran Hatam Vahdati Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran Ahmad Alinejad College of Farabi, University of Tehran, Iran Journal Article 2024 10 20 In this paper, we study the problem of describing the<br />form of Jordan generalized $d$-derivations on generalized module extension Banach algebras. As an application, we characterize the form of Jordan generalized $d$-derivations on $\theta$-Lau product of Banach algebras. Finally, we show that under some sufficient and necessary conditions, every Jordan generalized $d$-derivation on a generalized module extension Banach algebra is the sum of a generalized $d$-derivation and an antiderivation. generalized Jordan $d$-derivation generalized module extension Banach algebra $\theta$-Lau product of Banach algebras https://ijnaa.semnan.ac.ir/article_10478_72a946f6bbc35bde4ef8189f7d0d27d1.pdf