Symmetry of Syzygies of a System of Functional Equations Defining a Ring Homomorphism

I deal with an alienation problem for the system of two fundamental Cauchy functional equations with an unknown function f mapping a ring X into an integral domain Y and preserving binary operations of addition and multiplication, respectively. The resulting syzygies obtained by adding (resp. multiplying) these two equations side by side are discussed. The first of these two syzygies was first examined by Jean Dhombres in 1988 who proved that under some additional conditions concering the domain and range rings it forces f to be a ring homomorphism (alienation phenomenon). The novelty of the present paper is to look for sufficient conditions upon f solving the other syzygy to be alien.

Characterization and Stability of Multimixed Additive-Quartic Mappings: A Fixed Point Application

In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.

Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning

Probabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked to the symmetry of a system of functional equations’ transformation. Our objective is to propose a generic probabilistic functional equation that can cover most of the mathematical models addressed in the existing literature. The notable fixed-point tools are utilized to examine the existence, uniqueness, and stability of the suggested equation’s solution. Two examples are also given to emphasize the significance of our findings.

Some new common fixed point theorems for contractive selfmappings with applications

In this paper, we first prove a new common fixed point in general topological spaces with a [Formula: see text]-distance. From this result, we establish two common fixed points for two new classes of contractive selfmappings in complete bounded metric spaces. Furthermore, an application to a system of differential equations and another to a system of functional equations arising in dynamic programming are given.

Characterization, stability and hyperstability of multi-quadratic–cubic mappings

In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to a single equation. Applying a fixed point theorem, we study the generalized Hyers–Ulam stability of multi-quadratic–cubic mappings. As a result, we investigate the hyperstability of multi-quadratic–cubic mappings in some senses.

Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach

In this article, by using a new form of multi-quadratic mapping, we define multi-m-Jensen-quadratic mappings and then unify the system of functional equations defining a multi-m-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi-m-Jensen-quadratic functional equations. As a consequence, we show that every multi-m-Jensen-quadratic functional equation (under some conditions) can be hyperstable.

Hybrid Fixed Point Theorem with Applications to Forced Damped Oscillations and Infinite Systems of Fractional Order Differential Equations

In this manuscript, hybrid common fixed point results in the setting of a b -metric space are established. Our results generalized the results of Fisher, Khan, and Piri et al. for set-valued mapping in b -metric spaces. Applications to forced damped oscillations, infinite systems of fractional order differential equations, and system of functional equations are also studied. We construct an example to support our main result.