• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.179-189
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• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.491-502
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• 2016

In this paper, as a generalization of symmetric bi-derivations and symmetric bi-f-derivations of a lattice, we introduce the notion of symmetric bi-(f, g)-derivations of a lattice. Also, we define the isotone symmetric bi-(f, g)-derivation and obtain some interesting results about isotone. Using the notion of $Fix_a(L)$ and KerD, we give some characterization of symmetric bi-(f, g)-derivations in a lattice.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.441-451
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• 2019

In this paper, we introduce the notion of symmetric bi-f-derivation on subtraction algebra and investigated some related properties. Also, we prove that if D : X → X is a symmetric bi-f-derivation on X, then D satisfies D(x - y, z) = D(x, z) - f(y) for all x, y, z ∈ X.

• East Asian mathematical journal
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• v.36 no.1
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• pp.1-11
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• 2020

In this paper, we introduce the notion of symmetric bi-f-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if D is a symmetric bi-f-derivation of L, then D(x → y, z) = f(x) → D(y, z) for all x, y, z ∈ L.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.125-136
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• 2022

The goal of this paper is to introduce the notion of generalized symmetric bi-f-derivations in lattices and to study some properties of generalized symmetric f-derivations of lattice. Moreover, we consider generalized isotone symmetric bi-f-derivations and fixed sets related to generalized symmetric bi-f-derivations.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.443-451
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• 2016

In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.959-967
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• 2011

Let A be a Banach algebra and let f : $A{\times}A{\rightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{\times}A{\rightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.819-826
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• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.