Results 1 to 10 of about 156 (59)

A Parametric Functional Equation Originating from Number Theory [PDF]

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   +3 more sources

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

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

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   +3 more sources

A Levi–Civita Equation on Monoids, Two Ways [PDF]

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
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
exaly   +2 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

Geometric properties of basic hypergeometric functions

Journal of Difference Equations and Applications, 2014
In this paper we consider basic hypergeometric functions introduced by Heine. We study mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex ...
Agrawal, Sarita, Sahoo, Swadesh
exaly   +3 more sources

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

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