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Multi-Jensen and multi-Euler-Lagrange additive mappings
Abasalt Bodaghi,Amir Sahami 대한수학회 2024 대한수학회논문집 Vol.39 No.3
In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of $n$ equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.
General system of multi-sextic mappings and stability results
Abasalt Bodaghi 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and G\u{a}vru\c{t}a stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-$\beta$-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.
FUNDAMENTAL STABILITIES OF THE NONIC FUNCTIONAL EQUATION IN INTUITIONISTIC FUZZY NORMED SPACES
Bodaghi, Abasalt,Park, Choonkil,Rassias, John Michael Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
In the current work, the intuitionistic fuzzy version of Hyers-Ulam stability for a nonic functional equation by applying a fixed point method is investigated. This way shows that some fixed points of a suitable operator can be a nonic mapping.
Multi-derivations and some approximations
Abasalt Bodaghi,Hassan Feizabadi 대한수학회 2022 대한수학회논문집 Vol.37 No.3
In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers--Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.
An example for the non-stability of multi-additive-quadratic-cubic mappings
Abasalt Bodaghi 대한수학회 2024 대한수학회논문집 Vol.39 No.1
In this paper, we improve Corollary 1 of \cite{bras} and then present an example to show that the assertion in the mentioned corollary can not be valid in the singularity case.
General solution and Ulam-Hyers stability of viginti functional equations in multi-Banach spaces
Murali Ramdoss,Abasalt Bodaghi,Aruldass Antony Raj 충청수학회 2018 충청수학회지 Vol.31 No.2
In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.
STABILITY AND HYPERSTABILITY OF MULTI-ADDITIVE-CUBIC MAPPINGS IN INTUITIONISTIC FUZZY NORMED SPACES
( Elahe Ramzanpour ),( Abasalt Bodaghi ),( Alireza Gilani ) 호남수학회 2020 호남수학학술지 Vol.42 No.2
In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.
MODULE DERIVATIONS ON COMMUTATIVE BANACH MODULES
Amini, Massoud,Bodaghi, Abasalt,Shojaee, Behrouz Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup S, every module derivation of 𝑙<sup>1</sup>(S) into a reflexive module is inner.
MODULE AMENABILITY AND MODULE ARENS REGULARITY OF WEIGHTED SEMIGROUP ALGEBRAS
Asgari, Gholamreza,Bodaghi, Abasalt,Bagha, Davood Ebrahimi Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.3
For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.
A NEW TYPE OF THE ADDITIVE FUNCTIONAL EQUATIONS ON INTUITIONISTIC FUZZY NORMED SPACES
Arunkumar, Mohan,Bodaghi, Abasalt,Namachivayam, Thirumal,Sathya, Elumalai Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
In this paper, we introduce a new type of additive functional equations and establish the generalized Ulam-Hyers stability for it in intuitionistic fuzzy normed space by using direct and fixed point methods.