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E-Journal of Analysis and Applied Mathematics
ISSN 2544-9990 · EJAAM · 56 articles in the index
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Journal Article
Exploring new types of Hardy-Hilbert integral inequalities
This article explores two new types of Hardy-Hilbert integral inequalities constructed using flexible kernel functions. These functions are versatile due to the interplay of two or more parameters, as well as their asymmetric structural properties. Our proofs establish sharp and consistent upper…
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On the mean integral of the reciprocal and ratio of trigonometrically convex functions
Trigonometrically convex functions have recently emerged as an important class of functions in the field of convex analysis. Despite the growing interest, several aspects of their theory remain unexplored. In this article, we first establish lower and upper bounds for the mean integral of the…
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Weakly compact embedding of non-commutative symmetric spaces
In this paper, we prove that the embeddings of certain well-known symmetric spaces are weakly compact. Our main results concern noncommutative Lorentz and Marcinkiewicz spaces on finite von Neumann algebras.
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A note on fractional powers of first-order differential and difference operators in relation to fractional derivatives
This paper concentrates on fractional derivatives and fractional powers of first-order differential and difference operators. It is illustrated how fractional derivatives are related to fractional powers of a first-order positive operator with boundary condition. Moreover, difference formulas for…
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Solving Bratu's problem via the Chebyshev collocation method and non-polynomial spline functions with residual error
This paper investigates two numerical techniques for solving Bratu's problem: the Chebyshev polynomial method (CPs) with Gauss-Lobatto points and the non-polynomial spline function method (NPSFs). The main goal of the proposed approaches is to transform Bratu's equation with its associated mixed…
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Results on common fixed points in S_b-metric spaces
In this paper, we establish new common fixed point theorems for pairs of weakly compatible mappings within the framework of S_b-metric spaces. By introducing generalized contractive conditions, we demonstrate the existence and uniqueness of common fixed points for such self-mappings. Our results…
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A polynomially accelerated fixed-point iteration for vector problems
Fixed-point solvers are ubiquitous in nonlinear PDEs, yet their progress collapses whenever the Jacobian at the solution carries an eigenvalue arbitrarily close to one. We ask whether such stagnation can be removed without storing long histories or solving dense least squares. Under two…
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On the behavior of the solutions for certain neutral delay integro-differential equations
Some results are given on the behavior of solutions of scalar linear and constant coefficient neutral delay integro-differential equations. These results are obtained using two different real roots of the relevant characteristic equation. Finally, an example of solutions to neutral delay…
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Iterative methods for solving fractional differential equations using non-polynomial splines
In this work, a non-polynomial spline function is proposed to solve a linear fractional differential equation where the derivatives are in the Caputo sense. This approach transforms the fractional differential equation into a system of linear equations. The Gauss-Seidel and conjugate gradient…
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An asymptotic result for linear nonhomogeneous mixed type differential equation
We consider a nonhomogeneous linear mixed type differential equation with variable coefficients and establish an asymptotic result for its solutions. Our result is obtained by the use of a solution of the so-called generalized characteristic equation of the corresponding homogeneous linear mixed…
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The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$
The existence of $srg(99,14,1,2)$ has been a question of interest for several decades to the moment. In this paper, we consider the structural properties in general for the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$. In particular, we establish the lower bound for…
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Cards of fixed points of some Lotka-Volterra operators
The paper considers a special type of the Lotka-Volterra operator operating in a four-dimensional simplex. The tournament corresponding to this operator has four cyclic triples. All kinds of fixed point cards are built for it. It is proved which types of cards exist for Lotka-Volterra operators in…
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Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems
This paper presents the existence and uniqueness of the weak solution for the nonlinear system of sine-Gordon equations which describes DNA dynamics. An unconditionally stable second order difference scheme generated by the unbounded operator A2 corresponding to the system of sine-Gordon equations…
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On $p$-convexification of the Banach-Kantorovich lattice
Let $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. Let $(E,\|\cdot\|_{E})…
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The spacewise dependent source identification problem for the elliptic-telegraph differential equation with involution and Robin condition
In the present paper, the spacewise dependent source identification problem (SIP) for the elliptic-telegraph differential equation with involution and Robin condition is investigated. The theorem on stability estimates for the solution of this space-wise dependent SIP is established.
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Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models
The main purpose of this work is to establish a new links between the stochastic Cox-Ingersoll-Ross (CIR) model and the stochastic Rayleigh diffusion process (SRDP) and the links between the Vasicek Interest Rate (VIR) process and the stochastic Gompertz diffusion process (SGDP). These links focus…
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On the Schrödinger-parabolic equation with multipoint nonlocal boundary condition
The nonlocal boundary value problem for a Schrödinger-parabolic equation with multipoint nonlocal boundary conditions is examined. Stability estimates for the solution of this problem are established. Additionally, these stability estimates are applied to a mixed-type boundary value problem for the…
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Numerical algorithm for solving parabolic identification problem with mixed boundary condition
A source identification problem for a parabolic equation with mixed boundary condition is studied. Stability estimates for the solution of identification problem with mixed boundary conditions are obtained. Numerical algorithm for solving this inverse problem are proposed. Stability estimates for…
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Properties of the solution of some multipoint problems for integro-differential equation of Barbashin type
The nonlocal boundary value problems for the nonlinear integro-differential Barbashin equation with a partial derivative of the second order is studied. The solution of the problem is understood in the classical sense. The problem reduces to the equivalent Volterra integral equation with partial…
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The positivity of the differential operator generated by hyperbolic system of equations
In the present paper, the initial value problem for the hyperbolic system of equations with nonlocal boundary conditions is investigated. The positivity of the space operator generated by the given problem in interpolation spaces is established. The structure of interpolation spaces of this…