Results 1 to 10 of about 22 (22)
Further study on the Brück conjecture and some non-linear complex differential equations [PDF]
Arab Journal of Mathematical Sciences, 2021 Purpose – The purpose of this current paper is to deal with the study of non-constant entire solutions of some non-linear complex differential equations in connection to Brück conjecture, by using the theory of complex differential equation.
Dilip Chandra Pramanik, Kapil Roy
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A Parametric Functional Equation Originating from Number Theory
Annales Mathematicae Silesianae, 2022 Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ2 → S of the following parametric functional equation f(x1+x2+αy1y2,x1y2+x2y1+βy1y2)=f(x1,y1)f(x2,y2),f\left( {{x_1} + {x_2} + \alpha {y_1}{y_2},{x_1 ...
Mouzoun Aziz +2 more
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Sine Subtraction Laws on Semigroups
Annales Mathematicae Silesianae, 2023 We consider two variants of the sine subtraction law on a semi-group S. The main objective is to solve f(xy∗ ) = f(x)g(y) − g(x)f(y) for unknown functions f, g : S → ℂ, where x ↦ x* is an anti-homomorphic involution.
Ebanks Bruce
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On new stability results for composite functional equations in quasi-β-normed spaces
Demonstratio Mathematica, 2021 In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x)−f(y))=f(x+y)+f(x−y)−f(x)−f(y),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where ff maps from a (β,p)\left(\beta ...
Thanyacharoen Anurak +1 more
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The Cosine-Sine Functional Equation on Semigroups
Annales Mathematicae Silesianae, 2022 The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup.
Ebanks Bruce
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Entire solutions of two certain Fermat-type ordinary differential equations
Open Mathematics, 2023 In this article, we investigate the precise expression forms of entire solutions for two certain Fermat-type ordinary differential equations: (a0f+a1f′)2+(a0f+a2f′)2=p{\left({a}_{0}f+{a}_{1}{f}^{^{\prime} })}^{2}+{\left({a}_{0}f+{a}_{2}{f}^{^{\prime} })}^
Hu Binbin, Yang Liu
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Annales Mathematicae Silesianae, 2020 The paper consists of two parts. At first, assuming that (Ω, A, P) is a probability space and (X, ϱ) is a complete and separable metric space with the σ-algebra of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in ...
Baron Karol
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Alienation of Drygas’ and Cauchy’s Functional Equations
Annales Mathematicae Silesianae, 2021 Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation f(x+y)+g(x+y)g(x-y)=f(x)f(y)+2g(x)+g ...
Aissi Youssef +2 more
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A Levi–Civita Equation on Monoids, Two Ways
Annales Mathematicae Silesianae, 2022 We consider the Levi–Civita equation f(xy)=g1(x)h1(y)+g2(x)h2(y)f\left( {xy} \right) = {g_1}\left( x \right){h_1}\left( y \right) + {g_2}\left( x \right){h_2}\left( y \right) for unknown functions f, g1, g2, h1, h2 : S → ℂ, where S is a monoid.
Ebanks Bruce
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Meromorphic solutions of certain nonlinear difference equations
Open Mathematics, 2020 This paper focuses on finite-order meromorphic solutions of nonlinear difference equation fn(z)+q(z)eQ(z)Δcf(z)=p(z){f}^{n}(z)+q(z){e}^{Q(z)}{\text{Δ}}_{c}f(z)=p(z), where p,q,Qp,q,Q are polynomials, n≥2n\ge 2 is an integer, and Δcf{\text{Δ}
Liu Huifang, Mao Zhiqiang, Zheng Dan
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