Axioms, Volume 12, Issue 8 (August 2023) – 82 articles

The goal of this study is to refine some numerical radius inequalities in a novel way. The new improvements and refinements purify some famous inequalities pertaining to Hilbert space operators numerical radii. The inequalities that have been demonstrated in this work are not only an improvement over old inequalities but also stronger than them. Several examples supporting the validity of our results are provided as well. Full article

The goal of this paper is to investigate the existence and uniqueness of pseudo $\mathcal{S}$-asymptotically periodic mild solutions for a class of neutral fractional evolution equations with finite delay. We essentially use the fractional powers of closed linear operators, the semigroup theory and some classical fixed point theorems. Furthermore, we provide an example to illustrate the applications of our abstract results. Full article

The main purpose of this research paper is to discuss the solution of the singular two-dimensional pseudoparabolic equation by employing the double Sumudu-generalized Laplace transform decomposition method (DSGLTDM). We establish two theorems related to the partial derivatives. Furthermore, to investigate the relevance of the proposed method to solving singular two-dimensional pseudo parabolic equations, three examples are provided. Full article

In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with respect to a group of symmetries, and are interesting for their possible applications. Some conditions of the existence of topological isomorphisms between such algebras are obtained. We construct a class of countably generated algebras, where all normalized algebraic bases are equivalent. On the other hand, we find non-isomorphic classes of such algebras. In addition, we establish the conditions of the hypercyclicity of derivations in countably generated algebras of entire analytic functions of the bounded type. We use methods from the theory of analytic functions of several variables, the theory of commutative Fréchet algebras, and the theory of linear dynamical systems. Full article

Investment management is a common process and practice used for achieving a desirable investment goal or outcome. Unfortunately, the systematic variation of economic situations in the marketplace effects the continuous and frequent change of investment conditions and environment in which the investor should act and operate. Hence, the rules required for providing a reasonable quality of investment projects can be based only on the investor’s management strategy, intuition and practice. There exists various decision-making approaches to investment management, and simple additive weighting (SAW) is one of the most well-known multicriteria decision-making (MCDM) methods aiming to provide an optimal decision for the decision-maker when solving various real-life problems, particularly investment problems. In this paper, the fuzzy simple additive weighting (FSAW) method is applied in group decision-making to undertake capital investment expenditure for purchasing cars with the purpose of renting them out to the public. A numerical example illustrates the importance and effectiveness of the suggested approach with the aim of ranking alternatives, and, hence, determining the preferred alternative in the MCDM problem. Full article

In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the $\eta$-Ricci–Yamabe soliton ($\eta$-RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an $\eta$-RY soliton, an $\eta$-Ricci soliton, and an $\eta$-Yamabe soliton. Additionally, we consider the many circumstances under which a target manifold of Riemannian submersion is an $\eta$-RY soliton, an $\eta$-Ricci soliton, an $\eta$-Yamabe soliton, or a quasi-Yamabe soliton. We deduce a Poisson equation on a Riemannian submersion in a specific scenario if the potential vector field $\omega$ of the soliton is of gradient type =:grad$(\gamma )$ and provide some examples of an $\eta$-RY soliton, which illustrates our finding. Finally, we explore a number theoretic approach to Riemannian submersion with totally geodesic fibers. Full article

This article aims to obtain inequalities containing the unified Mittag–Leffler function which give bounds of integral operators for a generalized convexity. These findings provide generalizations and refinements of many inequalities. By setting values of monotone functions, it is possible to reproduce results for classical convexities. The Hadamard-type inequalities for several classes related to convex functions are identified in remarks, and some of them are also presented in last section. Full article

In this article, we present the use of a unique and common fixed point for a pair of mappings that satisfy certain rational-type inequalities in complex-valued b-metric spaces. We also provide applications related to authenticity concerns in integral equations. Our results combine well-known contractions, such as the Ćirić contraction and almost contractions. Full article

Our investigation is devoted to examining the existence, uniqueness, and multiplicity of positive solutions for a system of Hadamard fractional differential equations. This system is defined on an infinite interval and is subject to coupled nonlocal boundary conditions. These boundary conditions encompass both Hadamard fractional derivatives and Riemann–Stieltjes integrals, and the nonlinearities within the system are non-negative functions that may not be bounded. To establish the main results, we rely on the utilization of mathematical theorems such as the Schauder fixed-point theorem, the Banach contraction mapping principle, and the Avery–Peterson fixed-point theorem. Full article

In this paper, we refined the concept of past extropy measure for concomitants of order statistics from Farlie-Gumbel-Morgenstern family. In addition, cumulative past extropy measure and dynamic cumulative past extropy measure for concomitant of rth order statistic are also conferred and their properties are studied. The problem of estimating the cumulative past extropy is investigated using empirical technique. The validity of the proposed estimator has been emphasized using simulation study. Full article

In this study, we apply Hölder’s inequality, Jensen’s inequality, chain rule and the properties of convex functions and submultiplicative functions to develop an innovative category of dynamic Hardy-type inequalities on time scales delta calculus. A time scale, denoted by $\mathbb{T},$ is any closed nonempty subset of $\mathbb{R}.$ In time scale calculus, results are unified and extended. As particular cases of our findings (when $\mathbb{T}=\mathbb{R}$), we have the continuous analogues of inequalities established in some the literature. Furthermore, we can find other inequalities in different time scales, such as $\mathbb{T}=\mathbb{N},$ which, to the best of the authors’ knowledge, is a largely novel conclusion. Full article

This article employs the q-homotopy analysis transformation method (q-HATM) to numerically solve, subject to an integral condition, a fractional IBVP. The resulting numerical scheme is applied to solve, in which the exact solution is obtained, several test examples in order to illustrate its efficiency. Full article

In this paper, we consider the modified Mellin transform of the product of the square of the Riemann zeta function and the exponentially decreasing function, and we discuss its probabilistic and approximation properties. It turns out that this Mellin transform approximates the identical zero in the strip $\{s\in \mathbb{C}:1/2<\sigma <1\}$. Full article

Here, we center on the solvability of a fractional-order quadratic functional integro-differential equation with a nonlocal fractional-order integro-differential condition in the class of continuous functions. The maximal and minimal solutions will be discussed. The continuous dependence of the solutions on a few parameters will be examined. Finally, the problems of conjugate orders and integer orders, and some other problems and remarks will be discussed and presented. Full article

We study the existence/uniqueness of conformable fractional type impulsive nonlinear systems as well as the controllability of linear/semilinear conformable fractional type impulsive controlled systems. Using the conformable fractional derivative approach, we introduce the conformable controllability operator and the conformable controllability Gramian matrix in order to obtain the necessary and sufficient conditions for the complete controllability of linear impulsive conformable systems. We present a set of sufficient conditions for the controllability of the conformable semilinear impulsive systems. Full article

In this paper, a novel strategy is employed in which a degradation model affects the implied distribution of lifetimes differently compared to the traditional method. It is recognized that an existing link between the degradation measurements and failure time constructs the underlying time-to-failure model. We assume in this paper that the conditional survival function of a device under degradation is a piecewise linear function for a given level of degradation. The multiplicative degradation model is used as the underlying degradation model, which is often the case in many practical situations. It is found that the implied lifetime distribution is a classical mixture model. In this mixture model, the time to failure lies with some probabilities between two first passage times of the degradation process to reach two specified values. Stochastic comparisons in the model are investigated when the probabilities are changed. To illustrate the applicability of the results, several examples are given in cases when typical degradation models are candidates. Full article

Kurepa’s hypothesis for the left factorial has been an unsolved problem for more than 50 years. In this paper, we have proposed new equivalents for Kurepa’s hypothesis for the left factorial. The connection between the left factorial and the continued fractions is given. The new equivalent based on the properties of the integer part of real numbers is proven. Moreover, a new equivalent based on the properties of two well-known sequences is given. A new representation of the left factorial is listed. Since derangement numbers are closely related to Kurepa’s hypothesis, we made some notes about the derangement numbers and defined a new sequence of natural numbers based on the derangement numbers. In this paper, we indicate a possible direction for further research through solving quadratic equations. Full article

The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing $\chi$-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the $\chi$-curvature vanishes if and only if the H-curvature vanishes. Full article

In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constraints, and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions. Full article

This paper deals with a credit derivative pricing problem using the martingale approach. We generalize the conventional reduced-form credit risk model for a credit default swap market, assuming that the firms’ default intensities depend on the default states of counterparty firms and that the stochastic interest rate follows a jump-diffusion Cox–Ingersoll–Ross process. First, we derive the joint Laplace transform of the distribution of the vector process $(r_t,R_t)$ by applying piecewise deterministic Markov process theory and martingale theory. Then, using the joint Laplace transform, we obtain the explicit pricing of defaultable bonds and a credit default swap. Lastly, numerical examples are presented to illustrate the dynamic relationships between defaultable securities (defaultable bonds, credit default swap) and the maturity date. Full article

We are interested in the linear processes generated by dependent sequences under sub-linear expectation. Using the Beveridge–Nelson decomposition of linear processes and the inequalities, the moderate deviation principle for linear processes produced by an m-dependent sequence is established. We also prove the upper bound of the moderate deviation principle for linear processes produced by negatively dependent sequences via different methods from m-dependent sequences. These conclusions promote and improve the corresponding results from the traditional probability space to the sub-linear expectation space. Full article

Viscoelastic damping phenomena are ubiquitous in diverse kinds of wave motions of nonlinear media. This arouses extensive interest in studying the existence, the finite time blow-up phenomenon and various large time behaviors of solutions to viscoelastic wave equations. In this paper, we are concerned with a class of variable coefficient coupled quasi-linear wave equations damped by viscoelasticity with a long-term memory fading at very general rates and possibly damped by friction but provoked by nonlinear interactions. We prove a local existence result for solutions to our concerned coupled model equations by applying the celebrated Faedo-Galerkin scheme. Based on the newly obtained local existence result, we prove that solutions would exist globally in time whenever their initial data satisfy certain conditions. In the end, we provide a criterion to guarantee that some of the global-in-time-existing solutions achieve energy decay at general rates uniquely determined by the fading rates of the memory. Compared with the existing results in the literature, our concerned model coupled wave equations are more general, and therefore our theoretical results have wider applicability. Modified energy functionals (can also be viewed as certain Lyapunov functionals) play key roles in proving our claimed general energy decay result in this paper. Full article

In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem of a second-order differential equation containing a fractional derivative operator. The fractional differentiation operator was considered according to two definitions: Gerasimov-Caputo and Riemann-Liouville-Visualizations of the system of eigenfunctions, the biorthogonal system, and the distribution of eigenvalues on the real axis were presented. The numerical behavior of eigenvalues was studied depending on the order of the fractional derivative for both definitions of the fractional derivative. Full article

Tidal energy represents a clean and sustainable source of energy generation that can address renewable energy challenges, especially the global challenge of optimizing alternatives for stable supply. Although tidal stream energy extraction technology is in the early stages of development, it shows great potential compared to other renewable energy sources. The main objective of this research is to provide a digital tool for the optimization of the installation of turbines through fuzzy logic. The methodology in this study includes the design and development of a fuzzy-logic-based tool for this purpose. Design criteria included parameters such as salinity, temperature, currents, depth, and water viscosity, which affect the performance of tidal turbines. These parameters are obtained from the geographic location of the installation. A decision-making system is provided to support the tool. The designed fuzzy logic system evaluates the suitability of different turbine locations and presents the results through graphics and probability of success percentages. The results indicate that currents and temperatures are the most limiting factors in terms of potential turbine locations. The program provides a practical and efficient tool for optimizing the selection of tidal turbines and generating energy from ocean currents. This tool is evaluated and validated through different cases. With this approach, the aim is to encourage the development of tidal energy and its adoption worldwide. Full article

The Korteweg-de Vries equation models the formation of solitary waves in the context of shallow water in a channel. In our system, f or $p=2$ and $p=3$ (Korteweg-de Vries equations (KdV)) and (modified Korteweg-de Vries (mKdV) respectively), these equations have many applications in Physics. (gKdV) is a Hamiltonian system. In this article we investigate the generalized Korteweg-de Vries (gKdV) equation. A new topological approach is applied to prove the existence of at least one classical solution. The arguments are based upon recent theoretical results. Full article

This paper investigates the problem of entropy estimation for the generalized Rayleigh distribution under progressively type-II censored samples. Based on progressively type-II censored samples, we first discuss the maximum likelihood estimation and interval estimation of Shannon entropy for the generalized Rayleigh distribution. Then, we explore the Bayesian estimation problem of entropy under three types of loss functions: K-loss function, weighted squared error loss function, and precautionary loss function. Due to the complexity of Bayesian estimation computation, we use the Lindley approximation and MCMC method for calculating Bayesian estimates. Finally, using a Monte Carlo statistical simulation, we compare the mean square errors to examine the superiority of maximum likelihood estimation and Bayesian estimation under different loss functions. An actual example is provided to verify the feasibility and practicality of various estimations. Full article

In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions ${\mathcal{R}}_{\wp }$ associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp. Full article

Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations. This paper discusses accurate algebraic computations using a recent procedure to achieve an important factorization of these matrices with high relative accuracy and using alternative accurate methods. An algorithm to compute any minor of a Green matrix with high relative accuracy is also presented. The bidiagonal decomposition of the Hadamard product of Green matrices is obtained. Illustrative numerical examples are included. Full article

The pandemic caused by COVID-19 led to serious disruptions in the preventive efforts against other infectious diseases. In this work, a robust mathematical co-dynamical model of COVID-19, dengue, and HIV is designed. Rigorous analyses for investigating the dynamical properties of the designed model are implemented. Under a special case, the stability of the model’s equilibria is demonstrated using well-known candidates for the Lyapunov function. To reduce the co-circulation of the three diseases, optimal interventions were defined for the model and the control system was analyzed. Simulations of the model showed different control scenarios, which could have a positive or detrimental impact on reducing the co-circulation of the diseases. Highlights of the simulations included: (i) Upon implementation of the first intervention strategy (control against COVID-19 and dengue), it was observed that a significant number of single and dual infection cases were averted. (ii) Under the COVID-19 and HIV prevention strategy, a remarkable number of new single and dual infection cases were also prevented. (iii) Under the COVID-19 and co-infection prevention strategy, a significant number of new infections were averted. (iv) Comparing all the intervention measures considered in this study, it is possible to state that the strategy that combined COVID-19/HIV averted the highest number of new infections. Thus, the COVID-19/HIV strategy would be the ideal and optimal strategy to adopt in controlling the co-spread of COVID-19, dengue, and HIV. Full article

This study proposes a mathematical model that accounts for the interaction of bacteria, phages, and the innate immune response with a discrete time delay. First, for the non-delayed model we determine the local and global stability of various equilibria and the existence of Hopf bifurcation at the positive equilibrium. Second, for the delayed model we provide sufficient conditions for the local stability of the positive equilibrium by selecting the discrete time delay as a bifurcation parameter; Hopf bifurcation happens when the time delay crosses a critical threshold. Third, based on the normal form method and center manifold theory, we derive precise expressions for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to verify our theoretical analysis. Full article