• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.591-603
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• 2008

We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.513-522
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• 2012

In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.13-26
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• 1998

The purpose of this note is to study the relation between Heyting algebra and t-algebra which is the dual concept of BCK-algebra. We define t-algebra with binary operation ${\rhd}$ which is a generalization of the implication in the Heyting algebra, and define a bounded ness and commutativity of it, and then characterize a Heyting algebra and a Boolean algebra as a bounded commutative t-algebra X satisfying $x=(x{\rhd}y){\rhd}x$ for all $x,y{\in}X$.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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• pp.313-321
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• 2017

In this paper, we introduce the notion of a ${\ast}$-semiderivation on ${\ast}$-rings, and we try to extend some results for derivations of rings or near-rings to a more general case for ${\ast}$-semiderivations of prime ${\ast}$-rings.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.573-583
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• 2005

In this paper, all near-rings R are left near-rings and all representations of R are (right) R-groups. We start with a study of AR, almost AR and AGR rings which are motivated by the works on the Sullivan's Problem [10] and its properties. Next, for any R-group G, we introduce a notion of R-groups with M R-property and investigate their properties and some characterizations of these R-groups. Finally, for the faithful M R-property, we get a commutativity of near-rings and rings.

• The Mathematical Education
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• v.12 no.1
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• pp.1-3
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• 1973

In this paper, we want to verify some properties in tensor product. It is interesting to think semi-exact sequence in tensor Product by [3]. Moreover no hardness is there in process and we want to discuss the commutativity in tensor product. For a certain semi-exact sequence, if we product arbitrary Abelian group for each group then the tensor Product will do or not. Here, we have positive answer. At first we define the semi-exact sequence as following.

• The Pure and Applied Mathematics
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• v.21 no.3
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• pp.165-181
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• 2014

We establish a common n-tupled fixed point theorem for hybrid pair of mappings under new contractive condition. It is to be noted that to find n-tupled coincidence point, we do not use the condition of continuity of any mapping involved. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.135-151
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• 2008

The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on non complete Menger spaces. Our results extend, improve and generalize several known results in Menger spaces. We give formulas for total number of commutativity conditions for finite number of mappings.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.697-707
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• 2013

In this paper, we introduce the notion of permuting $n$-derivations in near-ring N and investigate commutativity of addition and multiplication of N. Further, under certain constrants on a $n!$-torsion free prime near-ring N, it is shown that a permuting $n$-additive mapping D on N is zero if the trace $d$ of D is zero. Finally, some more related results are also obtained.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.629-643
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• 2019

In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.