Results 171 to 180 of about 2,398,627 (204)

Multivalued nonlinear dominated mappings on a closed ball and associated numerical illustrations with applications to nonlinear integral and fractional operators. [PDF]

Heliyon
Rasham T, Panda SK, Basendwah GA, Hussain A.   +3 more
europepmc   +1 more source

Hyers–Ulam–Rassias Stability of a Linear Recurrence

Journal of Mathematical Analysis and Applications, 2005
The author considers a linear recurrence \[ x_{n+1}=a_nx_n+b_n,\qquad n\geq 0,\;x_0\in X \] where \((x_n)\) is a sequence in a Banach space \(X\) and \((a_n)\), \((b_n)\) are given sequences of scalars and vectors in \(X\), respectively. Then, a stability result is proved: Suppose that \(\varepsilon>0\), \(| a| >1\) and an arbitrary sequence \((b_n ...
Dorian Popa
exaly   +2 more sources

Hyers–Ulam and Hyers–Ulam–Rassias Stability of First-Order Nonlinear Dynamic Equations

Qualitative Theory of Dynamical Systems, 2021
We investigate Hyers-Ulam and Hyers-Ulam-Rassias stability of first-order nonlinear dynamic equations for functions defined on a time scale with values in a Banach ...
Martin Bohner, Alaa Hamza
exaly   +2 more sources

A Generalization of the Hyers–Ulam–Rassias Stability of Jensen's Equation

Journal of Mathematical Analysis and Applications, 1999
The following generalization of the stability of the Jensen's equation in the spirit of Hyers-Ulam-Rassias is proved: Let \(V\) be a normed space, \(X\) -- a Banach space, \(pa\). For the case \(p>1\) a corresponding result is obtained.
Yang-Hi Lee, Kil-Woung Jun
exaly   +3 more sources

A Generalization of the Hyers–Ulam–Rassias Stability of the Pexider Equation

Journal of Mathematical Analysis and Applications, 2000
Let \(V\) be a normed vector space and \(X\) a Banach space, and let \(f,g,h: V\to X\). The authors prove that the Pexider equation \[ f(x+y)= g(x)+h(y) \] is stable in the following sense: If there exists a real number \(p\neq 1\), such that \[ \bigl\|f(x+y)- g(x)-h(y) \bigr\|\leq\|x \|^p+ \|y\|^p \] for all \(x,y\in V\setminus \{0\}\), then there ...
Yang-Hi Lee, Kil-Woung Jun
exaly   +2 more sources

On the Hyers–Ulam–Rassias Stability of a Quadratic Functional Equation

Journal of Mathematical Analysis and Applications, 1999
The author examines the Hyers-Ulam-Rassias stability [see \textit{D. H. Hyers, G. Isac} and \textit{Th. M. Rassias}, Stability of functional equations in several variables, Birkhäuser, Boston (1998; Zbl 0907.39025)] of the quadratic functional equation \[ f(x-y-z)+f(x)+f(y)+f(z) = f(x-y)+f(y+z)+f(z-x) \] and proves that if a mapping \(f\) from a normed
Soon-Mo Jung
exaly   +2 more sources

Hyers–Ulam–Rassias Stability of an Equation of Davison

Journal of Mathematical Analysis and Applications, 1999
Let \(E_1\) be a normed algebra with a unit element, \(E_2\) be a Banach space and let \(f:E_1\rightarrow E_2\). In the paper the Hyers-Ulam-Rassias stability of the Davison functional equation \[ f(xy)+f(x+y)=f(xy+x)+f(y) \] is proved. As a consequence of the main theorem the authors obtain among others the following: Let \(\varepsilon\geq 0\) and \(p\
Prasanna K Sahoo, Soon-Mo Jung
exaly   +3 more sources

The Generalized Hyers–Ulam–Rassias Stability of a Cubic Functional Equation

Journal of Mathematical Analysis and Applications, 2002
The authors consider the functional equation \[ f(2x+y) +f(2x-y)=2f(x+y)+ 2f(x-y)+12f(x). \] They determine the general solution, which is of the form \(f(x)= B(x,x,x)\) where \(B\) is symmetric and additive in each variable. Moreover they investigate the stability properties of this equation.
Hark-Mahn Kim, Kil-Woung Jun
exaly   +2 more sources

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The Hyers–Ulam–Rassias stability of the pexiderized equations

Nonlinear Analysis: Theory, Methods & Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Park, Dal-Won, Lee, Yang-Hi
openaire   +2 more sources

Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation

Journal of Mathematical Analysis and Applications, 2000
The author studies the Hyers-Ulam-Rassias stability of a Jensen type functional equation \[ 3f((x+y+z)/3)+ f(x)+ f(y)+ f(z)= 2[ f((x+y)/2)+ f((y+z)/2)+ f((z+x)/2)]. \] The main result of this paper is the following: If the function \(f: X\to Y\) satisfies \[ \begin{multlined}\|3 f((x+y+z)/3)+ f(x)+ f(y)+ f(z)- 2[f((x+y)/2)+ f((y+z)/2)+ f((z+x)/2)]\|\\ \
Tiberiu Vasile Trif
exaly   +2 more sources