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We prove new Ulam stability results for the Davison functional equation, in the class of mappings h from a ring F into an m-Banach space. In this way, we complement several earlier outcomes, by extending them to the case of m-normed spaces. Our proofs are based on an earlier Ulam stability result obtained for some functional equation in a single variable. [ABSTRACT FROM AUTHOR]

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Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam's notion of stability is highly helpful since it provides a range of estimates between exact and approximate solutions. Using Brzdȩk's fixed point technique (FPT), we establish the stability of the following cubic type functional equations (CFUEQs): F ξ 1 3 + ξ 2 3 3 + F ξ 1 3 − ξ 2 3 3 = 2 F (ξ 1) + 2 F (ξ 2) , 2 F ξ 1 3 + ξ 2 3 2 3 = F (ξ 1) + F (ξ 2) for all ξ 1 , ξ 2 ∈ R . [ABSTRACT FROM AUTHOR]

The results for a new modeling integral boundary value problem (IBVP) using Caputo-Hadamard impulsive fractional integro-differential equations (C-HIFI-DE) with Banach space are investigated, along with the existence and uniqueness of solutions. The Krasnoselskii fixed-point theorem (KFPT) and the Banach contraction principle (BCP) serve as the basis of this unique strategy, and are used to achieve the desired results. We develop the illustrated examples at the end of the paper to support the validity of the theoretical statements. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using the Picard iteration method. Different from the previous works, our paper presents a new theory using the Hadamard fractional integral. We have proved the convergence of the solution of the averaged HIDSFOS to that of the standard HIDSFOS in the sense of the mean square and also in probability. Some examples are given at the end of this paper to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We propose a solution to the symmetric nonlinear Ψ -Caputo fractional integro differential equations involving non-instantaneous impulsive boundary conditions. We investigate the existence and uniqueness of the solution for the proposed problem. Banach contraction theorem is employed to prove the uniqueness results, while Krasnoselkii's fixed point technique is used to prove the existence results. Additionally, an example is used to explain the results. In this manner, our results represent generalized versions of some recent interesting contributions. [ABSTRACT FROM AUTHOR]

In this article, we employ a version of some fixed point theory (FPT) to obtain stability results for the symmetric functional equation (FE) of q-Wright affine functions in non-Archimedean (n , β) -Banach spaces (nArch (n , β) -BS). Furthermore, we give some interesting consequences of our results. In this way, we generalize several earlier outcomes. [ABSTRACT FROM AUTHOR]