Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra by Won-Gil Park, Jae-Hyeong Bae

“…We solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. …”
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Fixed point theorems for compatible mappings with applications to the solutions of functional equations arising in dynamic programmings by Nan-Jing Huang, Byung Soo Lee, Mee Kwang Kang

“…Some common fixed point theorems for compatible mappings are shown As an application, the existence and uniqueness of common solutions for a class of functional equations arising in dynamic programmings are discussed.…”
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A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces by Jie Shen, Miao Tian, Fang-Fang Guo, Jun-Nan Zhang

“…A new bundle-type approach for solving a class of functional equations is presented by combining bundle idea for nonsmooth optimization with common iterative process for functional equations. …”
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Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation by M. Janfada, R. Shourvazi

“…We study general solutions and generalized Hyers-Ulam-Rassias stability of the following 𝑛-dimensional functional equation ∑𝑓(𝑘𝑖=1𝑥𝑖∑)+(𝑘−2)𝑘𝑖=1𝑓(𝑥𝑖∑)=𝑘𝑖=1∑𝑘𝑗=1,𝑗>𝑖𝑓(𝑥𝑖+𝑥𝑗), 𝑘≥3, on non-Archimedean normed spaces.…”
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On a Unique Solution of the Stochastic Functional Equation Arising in Gambling Theory and Human Learning Process by Ali Turab, Awad A. Bakery, O. M. Kalthum S. K. Mohamed, Wajahat Ali

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On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n-Banach Spaces by Tian Zhou Xu, John Michael Rassias

“…The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation in n-Banach spaces by the direct method. …”
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Approximation of Mixed Euler-Lagrange σ-Cubic-Quartic Functional Equation in Felbin’s Type f-NLS by John Michael Rassias, Narasimman Pasupathi, Reza Saadati, Manuel de la Sen

“…In this research paper, the authors present a new mixed Euler-Lagrange σ-cubic-quartic functional equation. For this introduced mixed type functional equation, the authors obtain general solution and investigate the various stabilities related to the Ulam problem in Felbin’s type of fuzzy normed linear space (f-NLS) with suitable counterexamples. …”
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On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations by Paisan Nakmahachalasint

“…In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n-dimensional functional equation: f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj) when n>2. …”
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On a New Stability Problem of Radical nth-Degree Functional Equation by Brzdęk’s Fixed-Point Method by Dongseung Kang, Hoewoon B. Kim

“…In this paper, we introduce the radical nth-degree functional equation of the form f(xn+ynn)=f(x)+f(y) with a positive integer n, discuss its general solutions, and prove new Hyers-Ulam-type stability results for the equation by using Brzdęk’s fixed-point method.…”
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Stability of the n-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Non-Archimedean Normed Spaces by Yang-Hi Lee, Soon-Mo Jung, Themistocles M. Rassias

“…We will prove the stability of the functional equation 2f(∑i=1nxi)+∑1≤i,j≤n,i≠jf(xi-xj)=(n+1)∑i=1nf(xi)+(n-1)∑i=1nf(-xi) in non-Archimedean normed spaces.…”
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Ulam Stability and Non-Stability of Additive Functional Equation in IFN-Spaces and 2-Banach Spaces by Different Methods by N. Uthirasamy, K. Tamilvanan, Masho Jima Kabeto

“…This paper introduces a new dimension of an additive functional equation and obtains its general solution. The main goal of this study is to examine the Ulam stability of this equation in IFN-spaces (intuitionistic fuzzy normed spaces) with the help of direct and fixed point approaches and 2-Banach spaces. …”
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Absorbers: Definitions, properties and applications by G. Belitskii

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Quartic Functional Equation: Ulam-Type Stability in β,p-Banach Space and Non-Archimedean β-Normed Space by Ravinder Kumar Sharma, Sumit Chandok

“…In non-Archimedean β-normed space, we also verify Hyers–Ulam stability for the quartic functional equation stated. Many of the findings in the literature are improved and generalized by our findings.…”
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A General System of Euler–Lagrange-Type Quadratic Functional Equations in Menger Probabilistic Non-Archimedean 2-Normed Spaces by M. Eshaghi Gordji, M. B. Ghaemi, Y. J. Cho, H. Majani

“…We prove the generalized Hyers-Ulam-Rassias stability of a general system of Euler-Lagrange-type quadratic functional equations in non-Archimedean 2-normed spaces and Menger probabilistic non-Archimedean-normed spaces.…”
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Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) by Min Zhang

“…This work deals with Feigenbaum’s functional equation f(φ(x))=φp(f(x)), φ(0)=1, 0≤φ(x)≤1, x∈ [0, 1], where p≥2 is an integer, φp is the p-fold iteration of φ, and f(x) is a strictly increasing continuous function on [0, 1] that satisfies f(0)=0, f(x)<x, (x∈(0, 1]). …”
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Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation by M. Eshaghi Gordji, M. B. Ghaemi, G. H. Kim, Badrkhan Alizadeh

“…In this paper, we investigate the superstability of generalized (𝜃,𝜙)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.…”
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Ulam-Hyers Stability Results of λ-Quadratic Functional Equation with Three Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space by Ly Van An, Kandhasamy Tamilvanan, R. Udhayakumar, Masho Jima Kabeto, Ly Van Ngoc

“…In this paper, we introduce the λ-quadratic functional equation with three variables and obtain its general solution. …”
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On a Characterization of Exponential and Double Exponential Distributions by Reza Rastegar, Alexander Roitershtein

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Research on the Classification of Traditional Building Materials in Southern Fujian Using the Reflection Intensity Values of Ground-Based LiDAR by Tsung-Chiang Wu, Neng-Gang Kuan, Wei-Cheng Lu

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A convergent Deep Learning algorithm for approximation of polynomials by Després, Bruno

“…We start from the contractive functional equation proposed in [4], where it was shown that the polynomial solution of functional equation can be used to initialize a Neural Network structure, with a controlled accuracy. …”
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