Earthline Journal of Mathematical Sciences

On Geometry of Some Subspaces in Hornich Space

Xiaobin Wu — Fri, 13 Dec 2024 00:00:00 +0000

Let $\calH$ be the collection of all locally univalent analytic functions $f$ defined on the unit disk $\mathbb{D}$ with the normalization $f(0)=f^{\prime}(0)-1=0$, and $\calS\subseteq \mathcal{H}$ be the class of all univalent functions. For $f,g\in \mathcal{H}$ and $r\in \mathbb{C}$, the Hornich operators are defined as

$$r\odot f(z):=\int_0^z\{f'(\xi)\}^r\mathrm{d}\xi \quad\text{and}\quad f\oplus g(z):=\int_0^zf'(\xi)g'(\xi)\mathrm{d}\xi.$$

We study geometric properties of some subclasses of $\calS$ in the sense of the Hornich space $(\mathcal{H},\odot , \oplus )$. In fact, we prove that the classes of strongly convex functions of order $\beta$, Noshiro-Warschawski functions, and strongly Ozaki close-to-convex functions are all convex in $(\mathcal{H},\odot , \oplus )$, which generalize some known results. Meanwhile, for $M,N\in\calS$, let $T[M,N]:=\{(r,s)\in\mathbb{C}^2:r \odot f \oplus s \odot g\in N,\ for\ \forall f,g\in M \}$. We give the precise descriptions of $T[M,N]$ for some $M,N\in\calS$.

Optimal Debt Ratio and Investment-Consumption Strategies with Taxation in the Presence of Jump Risks

C. B. Ibe, O. E. Daudu — Mon, 16 Dec 2024 15:51:58 +0000

This paper derives an optimal debt ratio, consumption rate and investment strategies with taxation for an investor who invest under four background risks: investment, taxation, income and jump risks. The underlying assets considered in this paper are a riskless and risky asset. The risky asset is assumed to follow a jump-diffusion process. We also assume that the income growth rate and tax payment of the investor follow a jump-diffusion process. The aim of the investor is to derive the wealth-after-tax process. The wealth-after-tax process of the investor is taken to be the difference between the wealth-before-tax and the tax payment processes of the investor. The resulting wealth-after-tax process of the investor was solved using dynamic programming approach. As a result, we derive the optimal investment strategies, optimal debt ratio and optimal consumption rate for the investor over time by assuming that the investor chooses a power utility function. The optimal investment strategies were found to involve four components: a speculative portfolio, a tax risks hedging portfolio strategy, an income growth rate risks hedging portfolio strategy and a risk-free fund that holds only the riskless asset. Interestingly, we found that before loan is taken or given, the following must be considered: interest rate on loan to be taken or given, the nominal interest rate, income growth rate, coefficient of the investor willingness to bear the risk of taking debt. We also found that as the income growth rate of the investor increases, the debt profile of the investor decreases. We observe that as the coefficient of risk aversion with respect to debt ratio tends to unity, the amount of debt will be unbearable. It was also observed that the higher an investor willingness to bear the risk of taking debt, the smaller the optimal debt ratio of the investor over time. We further found that when tax rate increases, consumption rate decreases and vice versa. To ascertain the validity of our models, data were collected from six companies in Nigerian Stocks Exchange, and SPSS package was used to analyze the data. Some empirical results were obtained in this paper, using MATLAB software.

Differential Sandwich Theorems for Mittag-Leffler Function Associated with Fractional Integral Defined by Convolution Structure

Noor Yasser Jabir, Abbas Kareem Wanas — Wed, 18 Dec 2024 00:00:00 +0000

In this work, we use fractional integral and Mittag-Leffler function to obtain some results related to differential subordination and superordination defined by Hadamard product for univalent analytic functions defined in the open unit disk. These results are applied to obtain differential sandwich results. Our results extend corresponding previously known results.

Chatterjea-Type Contraction Mapping Theorem for Four Self-Mappings in Cone Pentagonal Metric Space

Clement Boateng Ampadu — Thu, 26 Dec 2024 00:00:00 +0000

In this paper we obtain a common fixed point theorem for four self mappings under Chatterjea contractive conditions in cone pentagonal metric space. We present an example in support of the main result. Some Corollaries conclude the paper.

On Some Relationships of Symmetric Sums: $u^n+v^n+w^n+(u+v+w)^n=k(u+v+w)(x^{n-1}+y^{n-1}+z^{n-1})$

Lao Hussein Mude — Mon, 30 Dec 2024 00:00:00 +0000

Let $u, v, w, x, y, k$ and $z$ be any integers and suppose that $n$ is a given exponent. This study focuses on the interplay between sums of four powers and product of symmetric sums. In particular, the Diophantine equation $u^n+v^n+w^n+(u+v+w)^n=k(u+v+w)(x^{n-1}+y^{n-1}+z^{n-1})$ is introduced and partially characterized within the set of integers for exponent $n=3$. Moreover, this research formulates a conjecture for the equation presented in the title.

Coefficient Estimates for Two New Subclasses of Bi-univalent Functions Involving Laguerre Polynomials

Elumalai Muthaiyan, Abbas Kareem Wanas — Mon, 30 Dec 2024 00:00:00 +0000

In this paper, we introduce two new subclasses of regular and bi-univalent functions using Laguerre polynomials. Then, we define some upper limits for the Taylor Maclaurin coefficients. In addition, the Fekete-Szegö problem for the functions of the new subclasses. Finally, we provide some corollaries for certain values of parameters.

On Extension of Existing Results on the Diophantine Equation: $\sum_{r=1}^n w_r^2+\frac{n}{3} d^2=3\left(\frac{n d^2}{3}+\sum_{r=1}^{\frac{n}{3}} w_{3 r-1}^2\right)$

Nyakebogo Abraham Osogo, Kimtai Boaz Simatwo — Sun, 05 Jan 2025 00:00:00 +0000

Let $w_r$ be a given sequence in arithmetic progression with common difference $d$. The study of diophantine equation, which are polynomial equations seeking integer solutions has been a very interesting journey in the field of number theory. Historically, these equations have attracted the attention of many mathematicians due to their intrinsic challenges and their significance in understanding the properties of integers. In this current study we examine a diophantine equation relating the sum of square integers from specific sequences to a variable $d$. In particular, on extension of existing results on the diophantine equation: $\sum_{r=1}^{n} w^2_r +\frac{n}{3}d^2= 3(\frac{nd^2}{3} +\sum^{\frac{n}{3}}_{n=1} w^{2}_{3r-1})$ is introduced and partially characterized.

A New Product for Soft Sets with its Decision-Making: Soft Gamma-Product

Aslıhan Sezgin, Eylül Şenyiğit, Murat Luzum — Tue, 07 Jan 2025 00:00:00 +0000

Soft sets provide a strong mathematical foundation for managing uncertainty and give creative answers to parametric data challenges. In soft set theory, soft set operations are essential components. The “soft gamma-product,” a novel product operation for soft sets, is presented in this study along with a detailed analysis of its algebraic features with respect to different kinds of soft equalities and subsets. We further explore the soft gamma-product’s relation with other soft set operations by examining its distributions over other soft set activities. Using the uni-int operator and uni-int decision function within the soft gamma-product for the uni-int decision-making approach, which finds an ideal collection of components from accessible possibilities, we end with an example showing the method's efficacy of many applications. Since the theoretical underpinnings of soft computing techniques are based on sound mathematical concepts, this study makes a substantial contribution to the literature on soft sets.

Interpolative Berinde Weak Cyclic Contraction Mapping Principle

Clement Boateng Ampadu — Mon, 20 Jan 2025 00:00:00 +0000

In this paper we introduce the notion of an interpolative Berinde weak cyclic operator. Additionally, we prove the existence and uniqueness of fixed point for such operators in metric space.

On the Solution of a Fractional-order Biological Population Model using q-Laplace Homotopy Analysis Method (qLHAM)

Oluwatope Richard Ojo — Thu, 23 Jan 2025 15:02:49 +0000

In this paper, we study a type of biological population model in its fractional order using the q-Laplace homotopy analysis method. This method, which combines the Laplace transform, q-calculus, and the homotopy analysis method developed by Shijun Liao in [11], is employed to provide approximate analytical solutions to the biological population model. Furthermore, we illustrate the dynamical behavior of this model graphically.