• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.239-246
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• 1999

The purpose of this paper is to prove the following result: Let R be a 2-torsion free noncommutative semi-prime ring and D:RlongrightarrowR a derivation. Suppose that $[[D(\chi),\chi],\chi]\in$ Z(R) holds for all $\chi \in R$. Then D is commuting on R.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.257-265
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• 2011

In this paper, we first prove a common fixed point theorem for generalized nonlinear contraction mappings in complete metric spaces there by generalizing and extending some known results. Then we present this result in the context of ordered metric spaces by using monotone non-decreasing mapping.

• East Asian mathematical journal
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• v.32 no.5
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• pp.701-716
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• 2016

We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.69-79
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• 2020

In this paper, we study the properties of T satisfying [CTC, T] = 0 for some conjugation C where [R, S] := RS - SR. In particular, we show that if T is normal, then [CTC, C] = 0. Moreover, the class of operators T satisfy [CTC, T] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T|C, |T|] = 0.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.21-28
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• 2015

Let R be a prime ring with center Z, I a nonzero ideal of R, and ${\sigma}$ a non-trivial automorphism of R such that $\{(x{\circ}y)^{\sigma}-(x{\circ}y)\}^n{\in}Z$ for all $x,y{\in}I$. If either char(R) > n or char (R) = 0, then R satisfies $s_4$, the standard identity in 4 variables.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.341-350
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• 2007

A dynamical system with a skew-commuting involution map is called a flip system. Every flip system on a subshift of finite type is represented by a pair of matrices, one of which is a permutation matrix. The transposition number of this permutation matrix is studied. We define an invariant, called the flip number, that measures the complexity of a flip system, and prove some results on it. More properties of flips on subshifts of finite type with symmetric adjacency matrices are investigated.

• East Asian mathematical journal
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• v.31 no.1
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• pp.77-89
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• 2015

We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under generalized non-linear contraction. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

• East Asian mathematical journal
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• v.18 no.1
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• pp.127-136
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• 2002

In this paper we obtain some fixed points theorems of expansive mappings and several necessary and sufficient conditions for the existence of common fixed points of families of self-mappings in metric spaces. Our results generalize and improve the main results of Fisher [1]-[5], Furi-Vignoli [6], $Is\'{e}ki$ [7], Jungck [8], [9], Kashara-Rhoades [10], Liu [13], [14] and Sharma and Strivastava [16].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.141-144
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• 2006

In this paper, using the notion of generalized metric (or D-metric) due to Dhage [3], we give new definition of M-fuzzy metric spaces and prove a common fixed point theorem for two mappings under the condition of weak compatible and R-weakly commuting mappings in complete M-fuzzy metric spaces.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.609-616
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• 2021

We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.