Papers by Abasalt Bodaghi
Annals of the University of Craiova - Mathematics and Computer Science Series
In this article, we unify the multi-quadratic mappings as a single functional equation. We also a... more In this article, we unify the multi-quadratic mappings as a single functional equation. We also apply a fixed point theorem to provide the Hyers-Ulam stability for this new multi-quadratic functional equation in non-Archimedean normed spaces.
Journal of Mathematical Inequalities
In this paper, we introduce a new quadratic functional equation. In light of this equation, we de... more In this paper, we introduce a new quadratic functional equation. In light of this equation, we define the multi-quadratic mappings and reduce the system of n equations defining the multi-quadratic mappings to a single equation. We also obtain some stability and hyperstability results concerning multi-quadratic mappings in the setting of random normed spaces.
Ukrainian Mathematical Journal, 2021
UDC 517.986 We correct some results presented in [M. Eshaghi Gordji, F. Habibian, A. Rejali, Ide... more UDC 517.986 We correct some results presented in [M. Eshaghi Gordji, F. Habibian, A. Rejali, Ideal amenability of module extension Banach algebras, Int. J. Contemp. Math. Sci., 2, No. 5, 213–219 (2007)] and, using the obtained consequences, we find necessary and sufficient conditions for the module extension to be -weakly amenable, where is a closed ideal of the Banach algebra and is a closed -submodule of the Banach -bimodule We apply this result to the module extension where are two Banach -bimodules.
Mathematics
The main and the most important objective of this paper is to nominate some new versions of sever... more The main and the most important objective of this paper is to nominate some new versions of several well-known results about fixed-point theorems such as Caristi’s theorem, Pant et al.’s theorem and Karapınar et al.’s theorem in the case of b-metric spaces. We use a new technique provided by Miculescu and Mihail in order to prove our theorems. Some illustrative applications and examples are given to strengthen our new findings and the main results.
Mathematica Slovaca
In this paper, we introduce and study the concepts of Jordan amenability and Jordan biflatness of... more In this paper, we introduce and study the concepts of Jordan amenability and Jordan biflatness of Banach algebras and compare those with the classical notions of amenability and biflatness. We also find some relations between Jordan amenability and the existence of Jordan approximate and virtual diagonals. These could be considered as Jordan versions of the classical results due to Johnson and Helemskii. We show that, for all C *-algebras, the concepts of amenability and Jordan amenability coincide.
Demonstratio Mathematica
Let S S be an inverse semigroup with the set of idempotents E E . In this article, we find necess... more Let S S be an inverse semigroup with the set of idempotents E E . In this article, we find necessary and sufficient conditions for the weighted semigroup algebra l 1 ( S , ω ) {l}^{1}\left(S,\omega ) to be module approximately amenable (contractible) and module character amenable (as l 1 ( E ) {l}^{1}\left(E) -module).
Filomat
In this paper, we define the multicubic-quartic and the multimixed cubic-quartic mappings and cha... more In this paper, we define the multicubic-quartic and the multimixed cubic-quartic mappings and characterize them. In other words, we unify the system of functional equations defining a multimixed cubic-quartic (resp., multicubic-quartic) mapping to a single equation, namely, the multimixed cubic-quartic (resp., multicubic-quartic) functional equation. We also show that under what conditions a multimixed cubic-quartic mapping can be multicubic, multiquartic and multicubic-quartic. Moreover, by using a fixed point theorem, we study the generalized Hyers-Ulam stability of multimixed cubic-quartic functional equations in non-Archimedean normed spaces. As a corollary, we show that every multimixed cubicquartic mapping under some mild conditions can be hyperstable. Lastly, we present a non-stable example for the multiquartic mappings.
Miskolc Mathematical Notes, 2021
In this article, we introduce the multi-additive-cubic mappings and then unify the system of func... more In this article, we introduce the multi-additive-cubic mappings and then unify the system of functional equations defining a multi-additive-cubic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of such equation. As a result, we show that the multi-additive-cubic functional equation can be hyperstable.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, 2020
In this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equati... more In this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2020
In this paper, we introduce $$n$$ -variables mappings which are mixed additive-quadratic in each ... more In this paper, we introduce $$n$$ -variables mappings which are mixed additive-quadratic in each variable. We show that such mappings can be described by a equation, namely, by a multi-mixed additive-quadratic functional equation. The main goal is to extend the applications of a fixed point method to establish the Hyers-Ulam stability for the multi-mixed additive-quadratic mappings.
International Journal of General Systems
Journal of Function Spaces
The aim of the current article is to characterize and to prove the stability of multi-Euler-Lagra... more The aim of the current article is to characterize and to prove the stability of multi-Euler-Lagrange quadratic mappings. In other words, it reduces a system of equations defining the multi-Euler-Lagrange quadratic mappings to an equation, say, the multi-Euler-Lagrange quadratic functional equation. Moreover, some results corresponding to known stability (Hyers, Rassias, and Gӑvruta) outcomes regarding the multi-Euler-Lagrange quadratic functional equation are presented in quasi- β -normed and Banach spaces by using the fixed point methods. Lastly, an example for the nonstable multi-Euler-Lagrange quadratic functional equation is indicated.
In this paper, among many other things we prove that two Banach algebras are both approximately c... more In this paper, among many other things we prove that two Banach algebras are both approximately character amenable if and only if their direct sum is approximately character amenable. Some examples of approximately left character amenable Banach algebras which are not left character amenable are given.
It is proved that every n-Jordan homomorphism between two commutative algebras is an n-ring homom... more It is proved that every n-Jordan homomorphism between two commutative algebras is an n-ring homomorphism when n is an arbitrary and fixed positive integer number. We employ this result to show that every involutive n-Jordan homomorphism between two commutative C *-algebras is automatically norm continuous.
Journal of Function Spaces, 2021
In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mapp... more In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.
Journal of Mathematical Extension, Aug 2, 2017
In this paper, we study derivations on the (projective) tensor product of Banach algebras. Among ... more In this paper, we study derivations on the (projective) tensor product of Banach algebras. Among other things, we show that under some mild conditions when the first cohomology group of A ⊗B with coefficients in (A ⊗J) * is zero, then B is J-weakly amenable, where J is a closed two-sided ideal in B. Also, we provide some concrete examples in which A ⊗B is ideally amenable.
For a Banach algebra A, a Banach A-bimodule E and a bounded Ba-nach A-bimodule homomorphism ∆ : E... more For a Banach algebra A, a Banach A-bimodule E and a bounded Ba-nach A-bimodule homomorphism ∆ : E −→ A, the notions of approximate ∆-amenability and ∆-contractibility for E are introduced. The general theory is developed and some hereditary properties are given. In analogy with approximate amenability and contractibility for Banach algebras, it is shown that under some mild conditions approximate ∆-amenability and approximate ∆-contractibility are the same properties.
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Papers by Abasalt Bodaghi