Abstract In this paper, we investigate three systems of quadratic trinomial functional equations, focusing on the existence and specific forms of finite-order transcendental entire solutions. Two systems, one formulated in C n \mathbb{C}^{n} with n ∈ N n\in\mathbb{N} and the other in C 2 \mathbb{C}^{2} , generalize and extend recent results from [Z. Tai, J. Long and X. Xiang, On entire solutions for several systems of quadratic trinomial Fermat type functional equations in C 2 \mathbb{C}^{2} , Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 (2024), 4, Paper No. 156]. To illustrate the validity and applicability of our findings, we provide concrete examples.
In the current investigation, we introduce a novel multimixed additive-quartic mapping as a system of mixed additive and quartic functional equations. Then we represent and characterize this system of functional equations as a single equation. We find some relations between this new definition and multi-additive and multi-quartic mappings by using linear and quartic conditions. Moreover, we show that each multimixed additive-quartic mapping can be reduced into either multi-additive or multi-quartic mapping. Furthermore, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations in the content of quasi-beta-2-Banach spaces. Eventually, we provide some known stability outcomes when the controller bound changes.
The aim of this work is to introduce generalized M-gamma and M-beta matrix functions based on the generalized M-series with matrix arguments. By employing the beta function, we define several important classes of hypergeometric matrix functions, including the generalized M-Gauss, M-confluent, M-Appell, and M-Lauricella hypergeometric matrix functions. Various particular cases are examined to illustrate how these newly defined functions extend and unify several existing results in matrix analysis. Furthermore, we establish fundamental properties such as integral representations and derivative formulas. As an application, the Laplace transforms of the M-Gauss and M-confluent hypergeometric matrix functions are derived, and their significance in fractional calculus is explored. The proposed framework offers a powerful analytical tool for solving fractional differential equations and significantly broadens the scope of matrix-valued special function theory.
Fibonacci extensions of several special polynomials, including Fibonacci-Bernoulli, Fibonacci-harmonic, Fibonacci-Euler, and Fibonacci-Hermite polynomials, have recently been studied, and numerous properties and relations of these polynomials have been thoroughly examined utilizing the content of the golden calculus. This paper aims to consider the generating functions of the Fibonacci-Gould-Hopper polynomials and the Gould-Hopper-based Fibonacci-Frobenius-sigmoid polynomials, from which we derive several beneficial relations and properties. These include explicit formulas, summation formulas, correlation formulas with the new and old Fibonacci-type polynomials, symmetric properties, recurrence relation, addition formulas, golden derivative properties, and golden integral representation for these polynomials. Moreover, graphical illustrations of the Fibonacci-Gould-Hopper polynomials and the Gould-Hopper-based Fibonacci-Frobenius-sigmoid polynomials are presented. Their numerical analyses are used to validate theoretical results and reveal distinctive scattering patterns in the distribution of their zeros across the complex plane, offering insights into their underlying analytic structure. Furthermore, interesting patterns in the zeros (real and complex zeros) distributions of these two new families of polynomials are examined and drawn, forming 2D and 3D structures. In addition, the approximate real and complex zeros of the mentioned polynomials for some special cases are presented in four tables. Lastly, four conjectures about the zeros of these polynomials are given.
In this paper, a weak convergence theorem is proved to find out the solution of variational inequality problem for a mapping which is monotone as well as Lipschitz continuous in Hilbert space. This result can also be used to determine the solutions of constrained convex optimization and split feasibility problems.
The key result in this paper shows that autocontinuity is a sufficient and necessary condition on a monotone measure such that convergence in measure of a sequence of measurable functions implies convergence of the corresponding sequence of seminormed fuzzy integrals of those measurable functions. Our work is an improvement of several previously published results.
In this paper, we focus on investigating the existence of mild solutions and the stability analysis of fractional evolution equations involving finite time delay and maxima. Our approach relies on tools such as the measure of non-compactness, the concept of p {{p}} -set contractions, and the Banach contraction principle. Additionally, we employ a generalized form of Gronwall's inequality to examine various types of stability. To demonstrate the applicability of our theoretical findings, a concrete example is provided.
Homogeneous and inhomogeneous biharmonic equation are considered on the n-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found for some sets of parameters.
In the work, the author derives an integral representation of the Gauss hypergeometric functions 2F(1)(a - 1/2, a; a + 1/2; z) by three approaches, applies the integral representation to give integral representations of several functions involving the inverse tangent function and including the Wilf function, and find out several combinatorial identities.
Let ( M 1 , g ) and ( M 2 , h ) be two Hermitian manifolds. Then the doubly warped product (abbreviated as DWP) Hermitian manifold of ( M 1 , g ) and ( M 2 , h ) is the product manifold M 1 x M 2 endowed with the warped product Hermitian metric G = f 2 2 g + f 1 2 h, where f and f 2 are positive smooth functions on M 1 and M 2, respectively. In this paper, the formula of altered Chern scalar curvature of DWP-Hermitian manifold is derived. The necessary and sufficient conditions for a DWP-Hermitian manifold to be K & auml;hler-like is obtained. It is also proved that a compact K & auml;hler-like DWP-Hermitian manifold is Chern flat when it has constant holomorphic sectional curvature or constant holomorphic bisectional curvature.
In this paper, we propose a novel concept of modified intuitionistic fuzzy double controlled metric spaces. Unlike traditional intuitionistic fuzzy bb-metric spaces, this framework integrates two non-comparable functions within the triangle inequality. To demonstrate the relevance and applicability of our results, we include illustrative examples and practical applications.
This paper focuses on establishing the existence of a capacity solution for the following anisotropicelliptic-parabolic system with variable exponent:{u(t)-Sigma(d)(i=1)[|u(xi)|(pi(x)-2)u(xi)/(1 + |u|)(gamma(pi(x)-1))](xi) = Theta(u)|del upsilon|(2) in Q(T) = ohm x (0, T), div(Theta(u)del upsilon) = 0 in Q(T), u = 0, upsilon = upsilon(0) on Gamma = partial derivative ohm x (0, T), u(., 0) = u(0) in ohm, where ohm is an open bounded subset of R-d with d > 2, Q(T) is the cylinder ohm x (0, T) with T > 0, 0 < gamma < 1, p(i) is an element of C(ohm) for all i = 1, . . . , d, Theta is an element of C(R), u(0)is an element of L-2(ohm), and upsilon(0)is an element of L-2(0, T; H-1(ohm)) boolean AND L-infinity(Q(T)).
We consider two Finsler p-Laplacian overdetermined problems in a bounded domain with smooth boundary, and show the existence and non-existence of solution based on comparison with radial solutions. By imposing some conditions we show that the solution of the overdetermined problem exists only when the domain is a Finsler ball.
In this paper we present some new general coincidence theory for maps with upper semicontinuous selections and then we use our results to generate some new minimax inequalities.
In this paper, we established new results of the product of a hypergeometric function with the multivariable 𝐴-function by applying definite integrals. Several other new and known results can be obtained from our main theorems.
This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum modulus points of an entire minimal surface S and the Lebesgue measure of the set { θ ∈ [ - π , π ] : log ∥ 𝐱 ( r e i θ ) ∥ > α log M ( r , S ) } {\{\theta\in[-\pi,\pi]:\log{\|\mathbf{x}(re^{i\theta})\|>\alpha\log{M(r,S)}}\}} ( 0 ≤ α < 1 {0\leq\alpha<1} ). The results of Arima and Baernstein are generalized. We also give examples showing that the obtained estimate is sharp.
The present work deals with the study of the dynamic behaviour of all vector solutions of a second order neutral delay difference system with constant coefficients of the form Δ 2 [ ϕ ( m ) - q ϕ ( m - l ) ψ ( m ) - q ψ ( m - l ) ] + [ b 1 b 2 b 3 b 4 ] [ ϕ ( m - τ ) ψ ( m - γ ) ] = 0 \Delta^{2}\begin{bmatrix}\phi(m)-q\phi(m-l)\\ \psi(m)-q\psi(m-l)\\ \end{bmatrix}+\begin{bmatrix}b_{1}&b_{2}\\ b_{3}&b_{4}\\ \end{bmatrix}\begin{bmatrix}\phi(m-\tau)\\ \psi(m-\gamma)\\ \end{bmatrix}=0 for m ≥ m 0 > ρ = max { l , τ , γ } {m\geq m_{0}>\rho=\max\{l,\tau,\gamma\}} by constructing the characteristic equations, where q ∈ ℝ - { 0 } {q\in\mathbb{R}-\{0\}} , b 1 , b 2 , b 3 , b 4 ∈ ℝ {b_{1},b_{2},b_{3},b_{4}\in\mathbb{R}} , l > 1 , τ , γ ∈ ℤ + {l>1,\tau,\gamma\in\mathbb{Z}^{+}} . Eight numerical examples are provided to validate the theoretical findings.
Consider the energy E-alpha[Sigma] = integral Sigma|p|(alpha) d Sigma, where Sigma is a surface in Euclidean space R-3 and alpha is an element of R. We prove that planes and spheres are the only stationary surfaces for E-alpha with constant Gauss curvature. We also characterize these surfaces assuming that a principal curvature is constant or that the mean curvature is constant.
The goal of this paper is to find spherical shells that contain all of the zeros of a unilateral polynomial with quaternionic coefficients. These bounds are derived using Ger & scaron;gorin-type results for the norms of the eigenvalues of a quaternionic matrix and matrix similarity. In addition to yielding some interesting implications, our results also bring certain classical results of Diaz-Barrero, Egozcue, Bidkham, and others into the quaternionic setting.
