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In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability for the quadratic type functional equation &f(x+y+2cz)+f(x+y-2cz)+c^2f(2x)+c^2f(2y) &=2[f(x+y)+c^2f(x+z)+c^2f(x-z)+c^2f(y+z)+c^2f(y-z)] {2.6 cm}…

Functional Analysis · Mathematics 2008-12-31 M. Eshaghi Gordji , H. Khodaei

The first order difference equation induced by the sequence of maps on $ \mathbb{C} $ has Hyers-Ulam stability where the limit of the geometric average of growth rate is convergent and not equal to one. %The average growth rate is a…

Dynamical Systems · Mathematics 2024-02-23 Young Woo Nam

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f, g, h, k$ are mappings from a symmetric orthogonality space to a Banach…

Functional Analysis · Mathematics 2021-07-23 M. Mirzavaziri , M. S. Moslehian

The stability problem in Ulam's sense has recently been explored in locally convex cone environments, as shown in \cite{ MNF, NR1, NR2}. In continuation of this research direction, our work examines the stability properties of the quadratic…

Functional Analysis · Mathematics 2025-08-19 J. -H. Bae , J. Mohammadpour , A. Najati

Using the direct method, we prove the generalised Hyers-Ulam stability of the following functional equation \begin{equation} \phi(x+y, z+w)+\phi(x-y, z-w)-2 \phi(x, z)-2 \phi(x, w)=0 \end{equation} in modular space satisfying the Fatou…

General Mathematics · Mathematics 2024-06-25 Abderrahman Baza , Mohamed Rossafi , Choonkil Park

We consider a Hilfer fractional differential equation with nonlocal Erd\'{e}lyi-Kober fractional integral boundary conditions. The existence, uniqueness and Ulam-Hyers stability results are investigated by means of the Krasnoselskii's fixed…

Classical Analysis and ODEs · Mathematics 2020-05-21 Mohamed I. Abbas

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s g(x) + t h(y)$ on various restricted domains such as inside balls, outside balls, and…

Functional Analysis · Mathematics 2021-07-23 Soon-Mo Jung , Mohammad Sal Moslehian , Prasanna K. Sahoo

Using fixed point methods, we prove the generalized Hyers--Ulam--Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen--type functional equation…

Functional Analysis · Mathematics 2009-12-21 A. Ebadian , Sh. Najafzadeh

We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.

Quantum Algebra · Mathematics 2016-11-22 Ludwik Dabrowski

Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $\lambda$, we study Hyers-Ulam stability of the global differential equation $Vy=\lambda…

Analysis of PDEs · Mathematics 2017-05-26 Maysam Maysami Sadr

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$f(2x+y)+f(2x-y)=4(f(x+y)+f(x-y))-{3/7}(f(2y)-2f(y))+2f(2x)-8f(x).$$

Functional Analysis · Mathematics 2008-12-31 M. Eshaghi Gordji

We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…

Functional Analysis · Mathematics 2021-03-26 Vladyslav Babenko , Vira Babenko , Oleg Kovalenko

In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…

Functional Analysis · Mathematics 2017-09-21 D. K. Patel , P. R. Patle , R. Pant , D. Gopal

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…

General Mathematics · Mathematics 2018-01-17 Deepesh Kumar Patel

In this paper, we obtain the general solution of the following functional equation f(3x + y + z) + f(x + 3y + z) + f(x + y + 3z) + f(x) + f(y) + f(z) = 6f(x + y + z): We establish the Hyers-Ulam-Rassias stability of the above functional…

Classical Analysis and ODEs · Mathematics 2015-06-09 Md. Nasiruzzaman

We extend Krasnoselskii's fixed point result to non-self-real functions. We find a new and simple proof for Hillam's result. In our approach, we don't assume the image of the related mapping to be compact or bounded. In this way, we extend…

Optimization and Control · Mathematics 2022-09-08 Hassan Khandani

In this paper, we establish the general solution of the functional equation $$f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0 cm}$$for fixed integers $n$ with $n\neq0,\pm1$ and investigate the generalized…

Functional Analysis · Mathematics 2008-12-31 S. Abbaszadeh , M. Eshaghi Gordji

In the present paper by the Fourier transform we show that every linear differential equations of $n$-th order has a solution in $L^1(\Bbb{R})$ which is infinitely differentiable in $\Bbb{R} \setminus \{0\}$. Moreover the Hyers-Ulam…

Functional Analysis · Mathematics 2020-05-08 H. Rezaei , Z. Zafarasa

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…

Commutative Algebra · Mathematics 2013-04-02 Katarzyna Kuhlmann , Franz-Viktor Kuhlmann

In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal type functional equation \begin{equation*}f(2x+y)+f(2x-y)=\frac{2f(x)f(y)\displaystyle{\sum_{\substack{k=0\\ \text{$k$ is even}}}^{…

Functional Analysis · Mathematics 2022-06-09 Idir Sadani