The Kneser conjecture (1955) was proved by Lovász (1978) using the Borsuk-Ulam theorem; all subsequent proofs, extensions and generalizations also relied on Algebraic Topology results, namely the Borsuk-Ulam theorem and its extensions. Only in 2000, Matoušek provided the first combinatorial proof of the Kneser conjecture. Here we provide a hypergraph coloring theorem, with a combinatorial proof...

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-reciiprocal functional equation in quasi-β-normed spaces. AMS Mathematics Subject Classification (2010): 39B82, 39B72

The generalized Hyers–Ulam–Rassias stability of generalized derivations on unital normed algebras into Banach bimodules is established. ∗2000 Mathematics Subject Classification. Primary 39B82; Secondary 46H25, 39B52, 47B47.

Abstract The main aim of this paper is to investigate various types Ulam stability and Mittag-Leffler linear differential equations first order with constant coefficients using the Aboodh transform method. We also obtain Hyers–Ulam constants these some examples illustrate our results are given.

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, prove an existence result. We also investigate the uniqueness solution using Banach contraction principle. Moreover, study Ulam-Hyers stability and generalized-Ulam-Hyers solutions. Some illustrative examples are presented.

We will apply a fixed point method for proving the Hyers–Ulam stability of the functional equation f(x+ y) = f(x)f(y) f(x)+f(y) .

We apply the Luxemburg–Jung fixed point theorem in generalized metric spaces to study the Hyers–Ulam stability for two functional equations in a single variable.

We study the generalized Hyers-Ulam stability of the functional equation f[x1,x2,x3]= h(x1+x2+x3). 2000 Mathematics Subject Classification. 39B22, 39B82.

Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...