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Showing papers in "The Korean Journal of Mathematics in 2019"


Journal ArticleDOI
TL;DR: In this article, soft semi-open sets are utilized to initiate seven new kinds of generalized soft compactness, namely soft semiLindel\"{o}fness, almost (approximately, mildly) soft semicompactness, and almost, mildly (soft semi-Lindel''{o]fness).
Abstract: The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-Lindel\"{o}fness, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi- Lindel\"{o}fness. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-Lindel\"{o}f spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.

13 citations


Journal ArticleDOI
TL;DR: This paper discusses the relations between intuitionistic fuzzy near UP-filters and their upper and lower $t$-(strong) level subsets in UP-algebras and proves their generalizations.
Abstract: The notions of intuitionistic fuzzy UP-subalgebras and intuitionistic fuzzy UP-ideals of UP-algebras were introduced by Kesorn et al. [13]. In this paper, we introduce the notions of intuitionistic fuzzy near UP-filters, intuitionistic fuzzy UP-filters, and intuitionistic fuzzy strong UP-ideals of UP-algebras, prove their generalizations, and investigate their basic properties. Furthermore, we discuss the relations between intuitionistic fuzzy near UP-filters (resp., intuitionistic fuzzy UP-filters, intuitionistic fuzzy strong UP-ideals) and their upper $t$-(strong) level subsets and lower $t$-(strong) level subsets in UP-algebras.

13 citations


Journal ArticleDOI
TL;DR: In this article, a sufficient condition is established under which an involution semigroup is non-finitely based, and this result is then applied to exhibit several examples of the desired opposite type.
Abstract: Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.

11 citations


Journal ArticleDOI
TL;DR: In this article, using local fractional integrals on fractal sets of real line numbers, the authors established new inequalities of Simpson's type based on generalized convexity, which they used to establish new inequalities based on the generalization of convexities.
Abstract: In this paper, using local fractional integrals on fractal sets $R^{\alpha }$ $\left( 0<\alpha \leq 1\right) $ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

11 citations


Journal ArticleDOI
TL;DR: In this paper, the strong metric dimension of zero-divisor graphs is studied by transforming the problem of finding the vertex cover number of a strong resolving graph into a more well-known problem.
Abstract: In this paper, we study the strong metric dimension of zero-divisor graph $\Gamma(R)$ associated to a ring $R$. This is done by transforming the problem into a more well-known problem of finding the vertex cover number $\alpha(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring $\mathbb{Z}_n$ of integers modulo $n$ and the ring of Gaussian integers $\mathbb{Z}_n[i]$ modulo $n$. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.

9 citations


Journal ArticleDOI
TL;DR: In this article, by virtue of the Fa\`a di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomial.
Abstract: In the paper, by virtue of the Fa\`a di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials.

8 citations


Journal ArticleDOI
TL;DR: In this paper, the Hadamard type integral inequalities for the Caputo $k-$fractional derivatives have been proved for convex functions with k-m-approximation.
Abstract: In this paper, first we obtain some inequalities of Hadamard type for $(h-m)-$convex functions via Caputo $k-$fractional derivatives. Secondly, two integral identities including the $(n+1)$ and $(n+2)$ order derivatives of a given function via Caputo $k-$fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo $k-$fractional derivatives have been proved.

6 citations


Journal ArticleDOI
TL;DR: In this article, the concept of pseudo-metric which is induced from a pseudo-valuation on KU-algebras was introduced and conditions for a real-valued function to be a pseudo valuation on a KU graph were provided.
Abstract: In this paper we have introduced the concept of pseudo-metric which we induced from a pseudo-valuation on KU-algebras and investigated the relationship between pseudo-valuations and ideals of KU-algebras Conditions for a real-valued function to be a pseudo-valuation on KU-algebras are provided

6 citations


Journal ArticleDOI
TL;DR: In this paper, the authors define and study the hypergeometric transmutation operators of the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam theory on $\mathbb{R}^d$ by using these operators, and give their properties and deduce simple proofs of the Plancherel formula.
Abstract: In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and ${}^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on $\mathbb{R}^d$. By using these operators we define the hypergeometric translation operator $\mathcal{T}^W_x, x \in \mathbb{R}^d$, and its dual ${}^t\mathcal{T}^W_x, x \in \mathbb{R}^d$, we express them in terms of the hypergeometric Fourier transform $\mathcal{H}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform $\mathcal{H}^W$. We study also the hypergeometric convolution product on $W$-invariant $L^p_{\mathcal{A}_k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

6 citations


Journal ArticleDOI
TL;DR: The notion of L-fuzzy semi-prime ideals and the radical of Fuzzy ideals in universal algebras are introduced and a theoretical study on their basic properties is made.
Abstract: In this paper, we introduce the notion of $ L- $fuzzy semi-prime ideals and the radical of $ L- $fuzzy ideals in universal algebras and make a theoretical study on their basic properties.

6 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the category of multiplicative Hom-Lie-Yamaguti superalgebras is closed under twisting by self-morphisms.
Abstract: (Multiplicative) Hom-Lie-Yamaguti superalgebras are defined as a $\mathbb{Z}_2$-graded generalization of Hom-Lie Yamaguti algebras and also as a twisted generalization of Lie-Yamaguti superalgebras. Hom-Lie-Yamaguti superalgebras generalize also Hom-Lie supertriple systems (and subsequently ternary multiplicative Hom-Nambu superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti superalgebras generalize Lie supertriple systems and Lie superalgebras. Hom-Lie-Yamaguti superalgebras are obtained from Lie-Yamaguti superalgebras by twisting along superalgebra even endomorphisms. We show that the category of (multiplicative) Hom-Lie-Yamaguti superalgebras is closed under twisting by self-morphisms. Constructions of some examples of Hom-Lie-Yamaguti superalgebras are given. The notion of an $nth$ derived (binary) Hom-superalgebras is extended to the one of an $nth$ derived binary-ternary Hom-superalgebras and it is shown that the category of Hom-Lie-Yamaguti superalgebras is closed under the process of taking $nth$ derived Hom-superalgebras.

Journal ArticleDOI
TL;DR: In this article, the categorical equivalence between crossed modules within groupoids and 2-groupoids was considered and the normality and quotient in these two categories were derived.
Abstract: The aim of this paper is to consider the categorical equivalence between crossed modules within groupoids and 2-groupoids; and then relate normality and quotient in these two categories.

Journal ArticleDOI
TL;DR: In this paper, the Hermite-Hadamard and Hermite Hadamard type inequalities for the exponentially convex functions via an extended generalized Mittag-Leffler function are presented.
Abstract: In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.

Journal ArticleDOI
TL;DR: This article presents the notion of e-fuzzy filters in an MS-Algebra and characterize in terms of equivalent conditions, and studies some properties of the space of all prime e- fuzzy filtering filters of anMS-algebra.
Abstract: In this article, we present the notion of $ e$-fuzzy filters in an MS-Algebra and characterize in terms of equivalent conditions. The concept of $ D $-fuzzy filters is studied and the set of equivalent conditions under which every $ e $-fuzzy filter is an $ D $-fuzzy filter are observed. Moreover we study some properties of the space of all prime $ e $-fuzzy filters of an MS-algebra.

Journal ArticleDOI
TL;DR: In this article, a general iterative algorithm was proposed to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces.
Abstract: In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Ricci solitons on almost CoKahler manifolds admit a contact vector field and the potential vector field is pointwise collinear to the reeb vector field.
Abstract: In the present paper is to classify Beta-almost ($\beta$-almost) Ricci solitons and $\beta$-almost gradient Ricci solitons on almost CoK\"ahler manifolds with $\xi$ belongs to $(k,\mu)$-nullity distribution. In this paper, we prove that such manifolds with $V$ is contact vector field and $Q\phi = \phi Q$ is $\eta$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a $(k,\mu)$-almost CoK\"ahler manifolds admitting $\beta$-almost gradient Ricci solitons is isometric to a sphere.

Journal ArticleDOI
TL;DR: In this paper, the authors considered a special hypergroup defined by Corsini and named it Corsini hypergroup, and investigated some of its properties and found a necessary and sufficient condition for the productional hypergroup of such hypergroups to be a Corsini supergroup.
Abstract: In this paper, we consider a special hypergroup defined by Corsini and we name it Corsini hypergroup. First, we investigate some of its properties and find a necessary and sufficient condition for the productional hypergroup of Corsini hypergroups to be a Corsini hypergroup. Next, we study its regular relations, fundamental group and complete parts. Finally, we characterize all Corsini hypergroups of orders two and three up to isomorphism.

Journal ArticleDOI
TL;DR: In this paper, the authors constructed a Sasakian manifold by the product of real line and K\"{a}hlerian manifold with exact K-a-hler form.
Abstract: In this paper, we construct a Sasakian manifold by the product of real line and K\"{a}hlerian manifold with exact K\"{a}hler form. This result demonstrates the close relation between Sasakian and K\"{a}hlerian manifold with exact K\"{a}hler form. We present an example and an open problem.

Journal ArticleDOI
TL;DR: It is proved that the lattice of the fuzzy filters in MS-algebras and the boosters are characterized in terms of boosters is isomorphic to the fuzzy ideal lattice.
Abstract: In this paper, we introduce the concept of $ \beta $-fuzzy filters in MS-algebras and $ \beta $-fuzzy filters are characterized in terms of boosters. It is proved that the lattice of $ \beta $-fuzzy filters is isomorphic to the fuzzy ideal lattice of boosters.

Journal ArticleDOI
TL;DR: In this article, the authors presented a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemmas for bounded analytic functions, and obtained a sharp upper bound for Hankel determinant.
Abstract: In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant $H_{2}(1)$. Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate necessary and sufficient conditions for elements in a semigroup of all transformations from a nonempty set to be left or right magnifying. But they do not consider the semigroup with respect to magnifications.
Abstract: Let $X$ be a nonempty set, $\rho$ be an equivalence on $X$, $T(X)$ be the semigroup of all transformations from $X$ into itself, and $T_{\rho}(X) = \{f \in T(X) \mid (x,y) \in \rho$ implies $((x)f, (y)f) \in \rho\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

Journal ArticleDOI
TL;DR: In this paper, a bilinear map on two unital algebraic tensor products was derived and a centralizer was obtained for the given maps on the given bilinearly maps.
Abstract: Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras and $\mathcal{A}\otimes\mathcal{B}$ be their algebraic tensor product. For two bilinear maps on $\mathcal{A}$ and $\mathcal{B}$ with some specific conditions, we derive a bilinear map on $\mathcal{A}\otimes\mathcal{B}$ and study some characteristics. Considering two $\mathcal{A}\otimes\mathcal{B}$ bimodules, a centralizer is also obtained for $\mathcal{A}\otimes\mathcal{B}$ corresponding to the given bilinear maps on $\mathcal{A}$ and $\mathcal{B}$. A relationship between orthogonal complements of subspaces of $\mathcal{A}$ and $\mathcal{B}$ and their tensor product is also deduced with suitable example.

Journal ArticleDOI
TL;DR: In this article, the convergence, equivalence of convergence, rate of convergence and data dependence results using a three-step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces were investigated.
Abstract: In the present paper, we investigate the convergence, equivalence of convergence, rate of convergence and data dependence results using a three step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces. Also we give non-trivial examples for the rate of convergence and data dependence results to show effciency of three step iteration process. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.

Journal ArticleDOI
TL;DR: In this paper, a new version of Steffensen inequality for the case of monotonic functions has been proposed, and conditions for validity of reverse to Steffen-inequivalent inequalities are given.
Abstract: In this paper, we provide a new version of Steffensen inequality for $p$-calculus analogue in [17,18] which is a generalization of previous results. Also, the conditions for validity of reverse to $p$-Steffensen inequalities are given. Lastly, we will obtain a generalization of $p$-Steffensen inequality to the case of monotonic functions.

Journal ArticleDOI
TL;DR: In this article, the authors consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, the edge Szeged index of a hydrocarbon family called Benzene ring was computed and denoted by $(BR)_{n\times n}$, where n is the number of atoms in the graph.
Abstract: Consider a connected molecular graph $G=(V,E)$ where $V$ is the set of vertices and $E$ is the set of edges. In $G$, vertices represent the atoms and edges represent the covalent bonds between atoms. In graph $G$, every edge (say) $e=uv$ will be connected by two atoms $u$ and $v$. The edge Szeged index is a topological index which has been introduced by Ivan Gutman. In this paper, we have computed edge Szeged indices of a hydrocarbon family called Benzene ring and is denoted by $(BR)_{n\times n}$.

Journal ArticleDOI
TL;DR: In this paper, the authors introduce the notion of residuated and Galois connections on adjoint triples and investigate their properties, and solve fuzzy relation equations and give their examples.
Abstract: In this paper, we introduce the notion of residuated and Galois connections on adjoint triples and investigate their properties. Using the properties of residuated and Galois connections, we solve fuzzy relation equations and give their examples.

Journal ArticleDOI
TL;DR: This study investigates understanding on conceptual and procedural knowledge of integration and to analyze errors of Riemann sum structure and presents the implications about improvement of integration teaching.
Abstract: Conceptual and procedural knowledge of integration is necessary not only in calculus but also in real analysis, complex analysis, and differential geometry. However, students show not only focused understanding of procedural knowledge but also limited understanding on conceptual knowledge of integration. So they are good at computation but don't recognize link between several concepts. In particular, Riemann sum is helpful in solving applied problem, but students are poor at understanding structure of Riemann sum. In this study, we try to investigate understanding on conceptual and procedural knowledge of integration and to analyze errors. Conducting experimental class of Riemann sum, we investigate the understanding of Riemann sum structure and so present the implications about improvement of integration teaching.

Journal ArticleDOI
TL;DR: In this article, the comparative growth properties of composite entire and meromorphic functions using relative $p}L^{\ast }$-order, relative $ p}L$-lower order and differential monomials, differential polynomials generated by one of the factors were established.
Abstract: In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_{p}L^{\ast }$-order, relative $_{p}L^{\ast }$-lower order and differential monomials, differential polynomials generated by one of the factors.

Journal ArticleDOI
TL;DR: In this paper, the authors define a local topological group-groupoid and prove that if the groupoid $G$ is a local groupoid, then the monodromy groupoid$Mon(G)$ of $G
Abstract: In this paper, we define a local topological group-groupoid and prove that if $G$ is a local topological group-groupoid, then the monodromy groupoid $Mon(G)$ of $G$ is a local group-groupoid.