Korean Journal of Mathematics

A note on Simpson $3/8$ rule for function whose modulus of first derivatives are $s$-convex function with application

Arslan Munir — 2024-09-30

Researchers continue to explore and introduce new operators, methods, and applications related to fractional integrals and inequalities. In recent years, fractional integrals and inequalities have gained a lot of attention. In this paper, firstly we established the new identity for the case of differentiable function through the fractional operator (Caputo-Fabrizio). By utilizing this novel identity, the obtained results are improved for Simpson second formula-type inequality. Based on this identity the Simpson second formula-type inequality is proved for the $s$-convex functions. Furthermore, we also include the applications to special means.

A brief review of predator-prey models for an ecological system with a different type of behaviors

Kuldeep Singh — 2024-09-30

The logistic growth model was developed with a single population in mind. We now analyze the growth of two interdependent populations, moving beyond the one-dimensional model. Interdependence between two species of animals can arise when one (the "prey") acts as a food supply for the other (the "predator"). Predator-prey models are the name given to models of this type. While social scientists are mostly concerned in human communities (where dependency hopefully takes various forms), predator-prey models are interesting for a variety of reasons. Some variations of this model produce limit cycles, an interesting sort of equilibrium that can be found in dynamical systems with two (or more) dimensions. In terms of substance, predator-prey models have a number of beneficial social science applications when the state variables are reinterpreted. This paper provides a quick overview of numerous predator–prey models with various types of behaviours that can be applied to ecological systems, based on a survey of various types of research publications published in the last ten years. The primary source for learning about predator–prey models used in ecological systems is historical research undertaken in various circumstances by various researchers. The review aids in the search for literature that investigates the impact of various parameters on ecological systems. There are also comparisons with traditional models, and the results are double-checked. It can be seen that several older predator–prey models, such as the Beddington–DeAngelis predator–prey model, the stage-structured predator–prey model, and the Lotka–Volterra predator–prey model, are stable and popular among academics. For each of these scenarios, the results are thoroughly checked.

Invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold with a quarter symmetric non-metric connection

Jasleen Kaur — 2024-09-30

The present work aims to introduce the geometry of invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold equipped with a quarter symmetric non-metric connection. The study establishes the characterization of integrability and parallelism of the distributions inherent in these submanifolds. Additionally, the conditions for distributions defining totally geodesic foliations on the invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifold are specified.

Characterizations of BiHom-alternative(-Leibniz) algebras through associated BiHom-Akivis algebras

Sylvain Attan — 2024-09-30

BiHom-Akivis algebras are introduced. It is shown that BiHom-Akivis algebras can be obtained either from Akivis algebras by twisting along two algebra morphisms or from a regular BiHom-algebra via the BiHom-commutator-BiHom-associator algebra. It is also proved that a BiHom-Akivis algebra associated to a regular BiHom-alternative algebra is a BiHom-Malcev algebra. Using the BiHom-Akivis algebra associated to a given regular BiHom-Leibniz algebra, a necessary and sufficient condition for BiHom-Lie admissibility of BiHom-Leibniz algebras is obtained.

On vector valued difference sequence spaces

Manoj Kumar — 2024-09-30

In the present paper, using the notion of difference sequence spaces, we introduce new kind of Cesàro summable difference sequence spaces of vector valued sequences with the aid of paranorm and modulus function. In addition, we extend the notion of statistical convergence to introduce a new sequence space $SC_1(\Delta,q)$ which coincides with $C_1^1(X,\Delta,\phi,\lambda,q)$ (one of the above defined Cesàro summable difference sequence spaces) under the restriction of bounded modulus function.

Hadamard-type inequalities on the coordinates for $(h_1, h_2, h_3)$-preinvex functions

Danish Malik — 2024-09-30

In the present paper, we define the class of $(h_1, h_2, h_3)$-preinvex functions on co-ordinates and prove certain new Hermite-Hadamard and Fejér type inequalities for such mappings. As a consequence, we derive analogous Hadamard-type results on convex and s-convex functions in three co-ordinates. We also discuss some intriguing aspects of the associated $H$ function.

On generalized Shen's square metric

Amr Soleiman — 2024-09-30

In this paper, following the pullback approach to global Finsler geometry, we investigate a coordinate-free study of Shen square metric in a more general manner. Precisely, for a Finsler metric $(M,L)$ admitting a concurrent $\pi$-vector field, we study some geometric objects associated with $\widetilde{L}(x,y)=\frac {(L+\mathfrak{B)}^2} {L}$ in terms of the objects of $L$, where $\mathfrak{B}$ is the associated $1$-form. For example, we find the geodesic spray, Barthel connection and Berwald connection of $\widetilde{L}(x,y)$. Moreover, we calculate the curvature of the Barthel connection of $\widetilde{L}$. We characterize the non-degeneracy of the metric tensor of $\widetilde{L}(x,y)$.

Quasi-cyclic self-dual codes with four factors

Hyun Jin Kim — 2024-09-30

In this study, we examine $\ell$-quasi-cyclic self-dual codes of length $\ell m$ over $\mathbb{F}_2$, provided that the polynomial $X^m-1$ has exactly four distinct irreducible factors in $\mathbb{F}_2[X]$. We find the standard form of generator matrices of codes over the ring $R \cong \mathbb{F}_q[X]/(X^m-1)$ and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths $2$ and $4$ over $R$.

Integral mean estimates for some operator preserving inequalities

Shabir Ahmad Malik — 2024-09-30

In this paper, some integral mean estimates for the polar derivative of a polynomial with complex coefficients are proved. We will see that these type of estimates are new in this direction and discuss their importance with respect to existing results comparatively. In addition, the obtained results provide valuable insights into the behavior of integrals involving operator preserving inequalities.

Multivalued fixed point theorem involving hybrid contraction of the Jaggi-Suzuki Type

Sirajo Yahaya — 2024-09-30

In this manuscript, a new multi-valued contraction is defined from a combination of Jaggi-type hybrid contraction and Suzuku-type hybrid contraction. Conditions for the existence of fixed points for such contractions in metric space are investigated. Moreover, some consequences are highlighted and discussed to indicate the significance of our proposed ideas. An example is given to support the assumptions of our theorems.

Cesàro type uncertain variables

Mehmet Şengönül — 2024-09-30

The main purpose of this study is to shed light on whether new types of uncertain variable sequences can be defined with the help of an infinite matrix. For this purpose, the first-order Cesàro matrix was used as an infinite matrix, and new types of uncertain variable sequences, called Cesàro-type uncertain variable sequences, were obtained. Theorems about uncertain variable sequences of Cesàro type have been included in this study, and some comparisons have been made. Thus, the gaps in the existing literature were filled.

Algebraic constructions of groupoids for metric spaces

Se Won Min — 2024-09-30

Given a groupoid $(X,*)$ and a real-valued function $d: X\to {\bf R}$, a new (derived) function $\Phi(X,*)(d)$ is defined as $[\Phi(X,*)(d)](x, y):= d(x*y) + d(y*x)$ and thus $\Phi(X,*): {\bf R}^X \to {\bf R}^{X^2}$ as well, where ${\bf R}$ is the set of real numbers. The mapping $\Phi(X,*)$ is an {\bf R}-linear transformation also. Properties of groupoids $(X,*)$, functions $d: X\to {\bf R}$, and linear transformations $\Phi(X,*)$ interact in interesting ways as explored in this paper. Because of the great number of such possible interactions the results obtained are of necessity limited. Nevertheless, interesting results are obtained. E.g., if $(X,*, 0)$ is a groupoid such that $x*y= 0= y*x$ if and only if $x=y$, which includes the class of all $d/BCK$-algebras, then $(X,*)$ is $*$-metrizable, i.e., $\Phi(X,*)(d) : X^2 \to X$ is a metric on $X$ for some $d: X\to {\bf R}$.

A new Banach space defined by absolute Jordan totient means

Canan Hazar Güleç — 2024-09-30

In the present study, we have constructed a new Banach series space $\left\vert \Upsilon ^{r}\right\vert _{p}^{u}$ by using concept of absolute Jordan totient summability $\left\vert \Upsilon ^{r},u_{n}\right\vert _{p}$ which is derived by the infinite regular matrix of the Jordan's totient function. Also, we prove that the series space $\left\vert \Upsilon ^{r}\right\vert _{p}^{u}$ is linearly isomorphic to the space of all $p$-absolutely summable sequences $\ell _{p}$ for $p\geq 1$. Moreover, we compute the $\alpha $-$,\beta $- and $\gamma $- duals of this space and construct Schauder basis for the series space $\left\vert \Upsilon^{r}\right\vert _{p}^{u}.$ Finally, we characterize the classes of infinite matrices $\left( \left\vert \Upsilon ^{r}\right\vert _{p}^{u},X\right) $ and $\left( X,\left\vert \Upsilon ^{r}\right\vert _{p}^{u}\right) ,$ where $X$ is any given classical sequence spaces $\ell _{\infty },$ $c,$ $c_{0}$ and $\ell _{1}$.

Cone $\mathfrak{C}$-class functions using $(CLR_{\Gamma \mathfrak{L} })$-property on cone $b$-normed spaces with application

K. Maheshwaran — 2024-09-30

In this article, we demonstrate the conditions for the existence of common fixed points $(CFP)$ theorems for four self-maps satisfying the common limit range $(CLR)$-property on cone $b$-normed spaces $(CbNS)$ via $\mathfrak{C}$-class functions. Furthermore, we have a unique common fixed point for two weakly compatible $ (WC)$ pairings. Towards the end, the existence and uniqueness of common solutions for systems of functional equations arising in dynamic programming are discussed as an application of our main result.