Nearly Quadratic Mappings over p-Adic Fields by M. Eshaghi Gordji, H. Khodaei, Gwang Hui Kim

“…We establish some stability results over p-adic fields for the generalized quadratic functional equation ∑k=2n∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir)+f(∑i=1nxi)=2n-1∑i=1nf(xi), where n∈N and n≥2.…”
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Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping by Hassan Azadi Kenary, Themistocles M. Rassias, H. Rezaei, S. Talebzadeh, Won-Gil Park

“…Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((−𝑥+𝑦+𝑧)/𝑟)=4𝑓(𝑥)+4𝑓(𝑦)+4𝑓(𝑧), where 𝑟 is a positive real number, in non-Archimedean normed spaces.…”
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Results on Uniqueness of Solution of Nonhomogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation by D. K. Igobi, U. Abasiekwere

“…In this work, we consider an initial value problem of a nonhomogeneous retarded functional equation coupled with the impulsive term. The fundamental matrix theorem is employed to derive the integral equivalent of the equation which is Lebesgue integrable. …”
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On Costas Sets and Costas Clouds by Konstantinos Drakakis

“…We abstract the definition of the Costas property in the context of a group and study specifically dense Costas sets (named Costas clouds) in groups with the topological property that they are dense in themselves: as a result, we prove the existence of nowhere continuous dense bijections that satisfy the Costas property on ℚ2, ℝ2, and ℂ2, the latter two being based on nonlinear solutions of Cauchy's functional equation, as well as on ℚ, ℝ, and ℂ, which are, in effect, generalized Golomb rulers. …”
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Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators by Azhar Hussain, Ahsan Ali, Vahid Parvaneh, Hassen Aydi

“…To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.…”
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Set-Valued SU-Type Fixed Point Theorems via Gauge Function with Applications by Amjad Ali, Monairah Alansari, Fahim Uddin, Muhammad Arshad, Awais Asif, Ghada Ali Basendwah

“…At the end, we will give an application to prove the existence behavior for the system of functional equation in dynamical system and integral inclusion.…”
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An allelopathic competition model with quorum sensing and delayed toxicant production by Paolo Fergola, Marianna Cerasuolo, Edoardo Beretta

“…The dynamics of a differential functional equation system representing an allelopathic competition is analyzed. …”
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Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods by H. Azadi Kenary, H. Rezaei, S. Talebzadeh, S. Jin Lee

“…The purpose of this paper is the generalized Hyers-Ulam stability for the following cubic functional equation: 𝑓(𝑚𝑥+𝑦)+𝑓(𝑚𝑥−𝑦)=𝑚𝑓(𝑥+𝑦)+𝑚𝑓(𝑥−𝑦)+2(𝑚3−𝑚)𝑓(𝑥),𝑚≥2 in various normed spaces.…”
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Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem by Ya-Ning Li, Hong-Rui Sun

“…We firstly prove that β-times integrated α-resolvent operator function ((α,β)-ROF) satisfies a functional equation which extends that of β-times integrated semigroup and α-resolvent operator function. …”
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On the Stability of Cubic and Quadratic Mapping in Random Normed Spaces under Arbitrary T-Norms by J. Vahidi, S. J. Lee, F. Fallah, R. Ahmadi

“…We prove the stability of some functional equations in the random normed spaces under arbitrary t-norms.…”
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Inclusions in a Single Variable in Ultrametric Spaces and Hyers-Ulam Stability by Magdalena Piszczek

“…As a consequence, we obtain stability results for the corresponding functional equations.…”
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On Approximately p-Wright Affine Functions in Ultrametric Spaces by Anna Bahyrycz, Janusz Brzdęk, Magdalena Piszczek

“…They are motivated by the notion of stability for functional equations.…”
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Hyers–Ulam–Rassias Stability of Additive Mappings in Fuzzy Normed Spaces by Jianrong Wu, Lingxiao Lu

“…In this paper, the Hyers–Ulam–Rassias stabilities of two functional equations, fax+by=rfx+sfy and fx+y+z=2fx+y/2+fz, are investigated in the framework of fuzzy normed spaces.…”
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Multivalued Fixed Point Theorems for Generalized Contractions and Their Applications by Muhammad Shoaib, Muhammad Sarwar

“…An application to functional equations is also discussed.…”
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Approximately Quintic and Sextic Mappings Form r-Divisible Groups into Ŝerstnev Probabilistic Banach Spaces: Fixed Point Method by M. Eshaghi Gordji, Y. J. Cho, M. B. Ghaemi, H. Majani

“…Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients form r-divisible groups into Ŝerstnev probabilistic Banach spaces.…”
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On a general Hyers-Ulam stability result by Costanz Borelli, Gian Luigi Forti

“…In this paper, we prove two general theorems about Hyers-Ulam stability of functional equations. As particular cases we obtain many of the results published in the last ten years on the stability of the Cauchy and quadratic equation.…”
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Convergence of the New Iterative Method by Sachin Bhalekar, Varsha Daftardar-Gejji

“…A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. …”
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Convoluted Fractional C-Semigroups and Fractional Abstract Cauchy Problems by Zhan-Dong Mei, Ji-Gen Peng, Jing-Huai Gao

“…We present two equivalent functional equations associated with convoluted fractional C-semigroup. …”
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α-Coupled Fixed Points and Their Application in Dynamic Programming by J. Harjani, J. Rocha, K. Sadarangani

“…Moreover, as an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.…”
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Functional-Type Caristi–Kirk Theorem on Menger Space and Application by Soumia Chaira, Mohammed Dahmouni, Abderrahim Eladraoui, Mustapha Kabil

“…Furthermore, we have functional equations as an application for the main theorem.…”
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