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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.
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.
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.
A. Bodaghi,J. M. Rassias,C. Park 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.3
A new form of a quadratic reciprocal functional equation is introduced. The Ulam-Hyers stability for this functional equation in non-Archimedean elds is investigated.
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.
THE GENERAL SOLUTION AND APPROXIMATIONS OF A DECIC TYPE FUNCTIONAL EQUATION IN VARIOUS NORMED SPACES
Arunkumar, Mohan,Bodaghi, Abasalt,Rassias, John Michael,Sathya, Elumalai Chungcheong Mathematical Society 2016 충청수학회지 Vol.29 No.2
In the current work, we define and find the general solution of the decic functional equation g(x + 5y) - 10g(x + 4y) + 45g(x + 3y) - 120g(x + 2y) + 210g(x + y) - 252g(x) + 210g(x - y) - 120g(x - 2y) + 45g(x - 3y) - 10g(x - 4y) + g(x - 5y) = 10!g(y) where 10! = 3628800. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in Banach spaces, generalized 2-normed spaces and random normed spaces by using direct and fixed point methods.
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.
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 ${\omega}$.
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.