The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...

I give a proof of the Borsuk-Ulam Theorem which I claim is a simplified version of the proof given in Bredon [1], using chain complexes explicitly rather than homology. Of course this is a matter of taste, and the mathematical content is identical, but in my opinion this proof highlights precisely where and how the contradiction arises. 1 Statements and Preliminaries Theorem 1.1 (Borsuk-Ulam). ...

In the current manuscript, we study uniqueness and Ulam-stability of solutions for sequential fractionalpantograph differential equations with nonlocal boundary conditions. The is es-tablished by Banach's fixed point theorem. We also define Ulam-Hyers stability theUlam-Hyers-Rassias mentioned problem. An example presented to illustrate main results.

In this paper, we establish the Mazur–Ulam theorem in the fuzzy strictly convex real normed spaces. Mathematics Subject Classification. Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

Let (X, τ, S) be a triple, where S is a compact, connected surface without boundary, and τ is a free cellular involution on a CW -complex X. The triple (X, τ, S) is said to satisfy the Borsuk-Ulam property if for every continuous map f : X −→ S, there exists a point x ∈ X satisfying f(τ(x)) = f(x). In this paper, we formulate this property in terms of a relation in the 2-string braid group B2(S...

This paper aims to study the existence and uniqueness of solution for nonlocal multiorder implicit differential equation involving Hilfer fractional derivative on unbounded domains a , ∞ ≥ 0 , in an applicable Banach...

In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...