Results 1 to 10 of about 129 (42)

Sine Subtraction Laws on Semigroups [PDF]

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
doaj   +3 more sources

Derivation Pairs on Rings and RNGs [PDF]

Annales Mathematicae Silesianae
We generalize a classical result about derivation pairs on function algebras. Specifically, we describe the forms of derivation pairs on rings and rngs (non-unital rings) which are not assumed to be commutative.
Ebanks Bruce
doaj   +3 more sources

A Kannappan-Cosine Functional Equation on Semigroups [PDF]

Annales Mathematicae Silesianae
In this paper we determine the complex-valued solutions of the Kannappan-cosine functional equation g(xyz0) = g(x)g(y) − f (x)f (y), x, y ∈ S, where S is a semigroup and z0 is a fixed element in S.
Jafar Ahmed, Ajebbar Omar, Elqorachi Elhoucien   +2 more
doaj   +3 more sources

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
doaj   +1 more source

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, Sintunavarat Wutiphol   +1 more
doaj   +1 more source

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, Zeglami Driss, Aissi Youssef   +2 more
doaj   +1 more source

Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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, Zeglami Driss, Fadli Brahim   +2 more
doaj   +1 more source