Korean Journal of Mathematics

Fuzzy lattice ordered group based on fuzzy partial ordering relation

2024-04-14T12:10:26+09:00

In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of $fl$-subgroups, quotients, and cosets of $fl$-groups and obtain some fundamental results for these fuzzy algebraic structures.

On the adapted partial differential equation for general diploid model of selection at a single locus

2024-02-24T15:59:23+09:00

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an $I^A I^A$ homozygote, the heterozygote $I^A I^B$ produces. W. Choi found the adapted partial differential equations for the density and operator of the frequency for one gene and applied this adapted partial differential equations to several diploid model. Also, he found adapted partial differential equations for the diploid model against recessive homozygotes and in case that the alley frequency occurs after one generation of selection when there is no dominance. (see. [1,2]).

In this paper, we find the adapted partial equations for the model of selection against heterozygotes and in case that the allele frequency changes after one generation of selection when there is overdominance. Finally, we shall find the partial differential equation of general type of selection at diploid model and it also shall apply to actual examples. This is a very meaningful result in that it can be applied in any model.

Generalized $\alpha$-Köthe Toeplitz duals of certain difference sequence spaces

2024-03-16T16:55:11+09:00

In this paper, we compute the generalized $\alpha$-K\"{o}the Toeplitz duals of the $X$-valued (Banach space) difference sequence spaces $E(X,\Delta)$, $E(X,\Delta_v)$ and obtain a generalization of the existing results for $\alpha$-duals of the classical difference sequence spaces $E(\Delta)$ and $E(\Delta_v)$ of scalars, $E \in \{ \ell_\infty,c,c_0 \}$. Apart from this, we compute the generalized $\alpha$-Köthe Toeplitz duals for $E(X,\Delta^r)\; r\geq0$ integer and observe that the results agree with corresponding results for scalar cases.

On the weakened hypotheses-based generalizations of the Enestr\"{o}m-Kakeya theorem

2024-02-14T17:38:03+09:00

According to the well-known Enestr\"{o}m-Kakeya Theorem, all the zeros of a polynomial $P(z)=\sum\limits_{s=0}^{n}a_sz^s$ of degree $n$ with real coefficients satisfying $a_n\geq a_{n-1}\geq\cdots\geq a_1\geq a_0>0$ lie in the complex plane $|z|\leq1.$ We provide comparable results with hypotheses relating to the real and imaginary parts of the coefficients as well as the coefficients' moduli in response to recent findings about an Enestr\"{o}m-Kakeya ``type" condition on real coefficients. Our findings so broadly extend the other previous findings.

Expansive type mappings in dislocated quasi-metric space with some fixed point results and application

2024-04-10T17:48:57+09:00

In this paper, we prove some new fixed point results for expansive type mappings in complete dislocated quasi-metric space. A common fixed point result is also established considering such mappings. Suitable examples are provided to demonstrate our results. The solution to a system of Fredholm integral equations is also established to show the applicability of our results.

Ruled surfaces generated by Salkowski curve and its Frenet vectors in Euclidean 3-space

2024-03-28T10:13:14+09:00

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

Faber polynomial coefficient estimates for analytic bi-univalent functions associated with Gregory coefficients

2024-02-02T15:23:04+09:00

In this work, we consider the function
\begin{equation*}
\Psi (z)=\frac{z}{\ln \left( 1+z\right) }=1+\sum_{n=1}^{\infty }G_{n}z^{n}
\end{equation*}
whose coefficients $G_{n}$ are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass $\mathcal{G}_{\Sigma }^{\lambda,\mu}\left( \Psi \right) $ of analytic bi-univalent functions subordinate to the function $\Psi $.

For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

A study on Milne-type inequalities for a specific fractional integral operator with applications

2024-02-17T01:47:14+09:00

Fractional integral operators have been studied extensively in the last few decades by various mathematicians, because it plays a vital role in the developments of new inequalities. The main goal of the current study is to establish some new Milne-type inequalities by using the special type of fractional integral operator i.e Caputo Fabrizio operator. Additionally, generalization of these developed Milne-type inequalities for $s$-convex function are also given. Furthermore, applications to some special means, quadrature formula, and $q$-digamma functions are presented.

A $(k,\mu)$-contact metric manifold as an $\eta-$Einstein soliton

2024-04-08T14:43:45+09:00

The aim of the paper is to study an $\eta$-Einstein soliton on $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold. At first, we establish various results related to $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold that exhibit an $\eta$-Einstein soliton. Next we study some curvature conditions admitting an $\eta$-Einstein soliton on $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold. Furthermore, we consider specific conditions associated with an $\eta$-Einstein soliton on $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold. Finally, we show the existance of an $\eta$-Einstein soliton on $(k,\mu)$-contact metric manifold.

Some fixed point results on double controlled cone metric spaces

2024-05-15T02:50:50+09:00

In this text, we investigate some fixed point results in double-controlled cone metric spaces using several contraction mappings such as the B-contraction, the Hardy-Rogers contraction, and so on. Additionally, we prove the same fixed point results by using rational type contraction mappings, which were discussed by the authors Dass. B. K and Gupta. S. Also, a few examples are included to illustrate the results. Finally, we discuss some applications that support our main results in the field of applied mathematics.

Note on Newton-type inequalities involving tempered fractional integrals

2024-04-13T19:50:40+09:00

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of H\"{o}lder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.