Type Functional Equation Research Articles

Stability and nonstability of the radical Drygas type functional equation

Stability and nonstability of the radical Drygas type functional equation

Hyers–Ulam stability of the Drygas type functional equation

Hyers–Ulam stability of the Drygas type functional equation

On entire solutions for several systems of quadratic trinomial Fermat type functional equations in $${\mathbb {C}}^2$$

On entire solutions for several systems of quadratic trinomial Fermat type functional equations in $${\mathbb {C}}^2$$

Stability Result in Lattice Random Normed Space

We use the direct method to study the generalized Hyers-Ulam stability of a mixed type(cubic-quartic) functional equation for all , in LRN-space.

All solutions to a Schröder type functional equation

All solutions to a Schröder type functional equation

Steklov Type Operators and Functional Equations

Abstract We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.

Fuzzy stability of mixed type functional equations in Modular spaces

In this article, our aim is to find some stability results for mixed type cubic and quartic functional equations in fuzzy modular spaces using the fundamental results of fixed-point theory. The fixed point method provides one of the effective techniques that can be used to investigate the fuzzy stability of a mixed type cubic and quartic functional equations.

Stability results of mixed type functional equations in modular spaces and 2-Banach spaces ∗

In this paper, we investigate the generalized Hyers-Ulam-Stability of additive and quartic functional equations in modular spaces with and without the △2-condition using the direct method and also in 2-Banach Spaces.

Fixed point approach to the stability of a cubic and quartic mixed type functional equation in non-archimedean spaces

Fixed point approach to the stability of a cubic and quartic mixed type functional equation in non-archimedean spaces

Shifted Legendre method for solutions of Riccati type functional differential equations and application of RL circuit model

AbstractIn order to solve the Riccati type functional differential equations under mixed condition, this research suggests a collocation approach based on shifted Legendre polynomials. These equations are seen in physics and electronic sciences. By means of the evenly spaced collocation points, the shifted Legendre polynomials, their derivatives and matrix forms, the method is constructed. It reduces the problem into a system nonlinear algebraic equations. Error analysis is made. The method is applied to numerical examples and their results are compared with other methods from literature. And also, the method is applied to nonlinear RL electrical circuit model. The results show that the method is effective.

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods.

Hyers Stability in Generalized Intuitionistic P-Pseudo Fuzzy 2-Normed Spaces

In this article, we defined the generalized intuitionistic P-pseudo fuzzy 2-normed spaces and investigated the Hyers stability of m-mappings in this space. The m-mappings are interesting functional equations; these functional equations are additive for m = 1, quadratic for m = 2, cubic for m = 3, and quartic for m = 4. We have investigated the stability of four types of functional equations in generalized intuitionistic P-pseudo fuzzy 2-normed spaces by the fixed point method.

Stability of Cauchy-Jensen Type Functional Equation in (2, α)–Banach Spaces

In this paper, we investigate some stability and hyperstability results for the following Cauchy-Jensen functional equation fx+y 2+fx−y 2=f(x) in (2,α)-Banach spaces using Brzd¸ek and Ciepliński’s fixed point approach.

Non-periodic solutions of the Goła̧b–Schinzel type functional equation

We determine the solutions of the Goła̧b-Schinzel type functional equation in the class of non-periodic functions. Applying this result we give a positive answer to the problem raised by E. Jabłońska (Aequationes Math 87:125–133, 2014).

Approximate solution of a generalized multi-quadratic type functional equation in Lipschitz spaces

It is well-known that the Lipschitz stability originated from the paper [32] of J. Tabor. In this work, we establish the general solution of the new class of generalized multi-quadratic functional equationf(x1,…,xi−1,xi+kyi,xi+1,...,xn)+f(x1,…,xi−1,xi−kyi,xi+1,…,xn)=f(x1,…,xi−1,xi+ℓyi,xi+1,…,xn)+f(x1,…,xi−1,xi−ℓyi,xi+1,…,xn)+2(k2−ℓ2)f(x1,...,xi−1,yi,xi+1,...,xn),xi,yi∈G,i∈{1,...,n} where k,ℓ are two fixed integers with k≠±ℓ and G is an Abelian group. Under some natural conditions, we prove the stability of the above equation in Lipschitz spaces. Moreover, some results concerning the stability of the generalized multi-quadratic type functional equation in the Lipschitz norms are presented. Our main results improve and generalize results obtained in [5,10–12,25–27].

On the Generalized Quadratic-Quartic Cauchy Functional Equation and its Stability over Non-Archimedean Normed Space

Functional equation plays a very important and interesting role in the area of mathematics, which involves simple algebraic manipulations and through which one can arrive an interesting solution. The theory of functional equations is also used in the development of other areas such as analysis, algebra, Geometry etc., the new methods and techniques are applied in solving problem in Information theory, Finance, Geometry, wireless sensor networks etc., In recent decades, the study of various types of stability of a functional equation such as HUS (Hyers-Ulam stability), HURS (Hyers-Ulam-Rassias stability) and generalized HUS of different types of functional equation and also for mixed type were discussed by many authors in various space. The problem of the stability of different functional equations has been widely studied by many authors, and more interesting results have been proved in the classical case (Archimedean). In recent years, the analogues results of the stability problem of these functional equations were investigated in non-Archimedean space. The aim of this study is to investigate the HUS of a mixed type of general Quadratic-Quartic Cauchy functional equation in non-Archimedean normed space. In this current article, we prove the generalized HUS for the following Quadratic-Quartic Cauchy functional equation over non-Archimedean Normed space.<img src=image/13428783_01.gif>

Non-Archimedean approximation of the m-Apollonius type functional equation

Throughout this paper, using the fixed point and direct methods, the generalized Hyers–Ulam stability of the following [Formula: see text]-Appolonius type functional equation [Formula: see text] has been proven, where [Formula: see text] is a positive integer greater than [Formula: see text], in non-Archimedean normed spaces.

Dirichlet series satisfying a Riemann type functional equation and sharing one set

In 2011, Li [A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation. Adv Math. 2011;226(5):4198–4211] proved that if two L-functions and satisfy the same functional equation with and for two distinct finite complex numbers and then We prove that if two L-functions and have positive degree and satisfy the same functional equation with and for a finite set where and are three distinct finite complex values, then The main results of this paper are concerning some questions posed by Gross [Factorization of meromorphic functions and some open problems. Complex Analysis, Kentucky 1976 (Proc.Conf.); Berlin: Springer-Verlag; 1977. p. 51–69. (Lecture Notes in Mathematics; 599)].

On Solutions and Stability of Stochastic Functional Equations Emerging in Psychological Theory of Learning

We show how to apply the well-known fixed-point approach in the study of the existence, uniqueness, and stability of solutions to some particular types of functional equations. Moreover, we also obtain the Ulam stability result for them. The functional equations that we consider can be used to explain various experiments in mathematical psychology and arise in a natural way in the stochastic approach to the processes of perception, learning, reasoning, and cognition.

Fermat type functional equations, several complex variables and Euler operator

Fermat type functional equations, several complex variables and Euler operator