Mahmoud, Ayman M. Tunç, Cemil
Published in
Advances in Pure and Applied Mathematics

In this paper, by defining Lyapunov functionals, we investigate proper sufficient conditions for the uniform stability of the zero solution, and also for the uniform boundedness and uniform ultimate boundedness of all solutions of a certain third-order nonlinear vector delay differential equation of the type X˙˙˙ + AX˙˙ + G(X˙) + H(X(t - r)) = P(t)...

Mishra, Pawan K. Sreenadh, Konijeti
Published in
Advances in Pure and Applied Mathematics

In this paper, we show the existence and multiplicity of nontrivial non-negative solutions of the fractional p-Kirchhoff problem M∫ ℝ 2n |u(x)-u(y)| p |x-y| n+ps d x d y(-Δ) p s u=λf(x)|u| q-2 u+g(x)|u| r-2 uinΩ,u=0inℝ n ∖Ω,$ M\Bigg (\int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+ps}}\,dx\,dy\Biggr )(-\Delta )^{s}_p u =\lambda f(x)|u|^{q-2}u...

Baklouti, Ali Nomura, Takaaki
Published in
Advances in Pure and Applied Mathematics

Ghabi, Rabiaa Mili, Maher
Published in
Advances in Pure and Applied Mathematics

In this paper, we consider the generalized Fourier transform associated with the Jacobi–Cherednik operator on ℝ and we give conditions of quite different kind for a function to have a transform belonging to certain Lp-classes.

Shpakivskyi, Vitalii
Published in
Advances in Pure and Applied Mathematics

Let 𝔸nm be an arbitrary n-dimensional commutative associative algebra over the field of complex numbers with m idempotents. Let e1 = 1, e2, e3 be elements of 𝔸nm which are linearly independent over the field of real numbers. We consider monogenic (i.e., continuous and differentiable in the sense of Gateaux) functions of the variable xe1 + ye2 + ze3...

Narasimman, P.
Published in
Advances in Pure and Applied Mathematics

In this paper, we obtain the general solution and we study the generalized Hyers–Ulam stability of the mixed type additive-quadratic functional equation f(-x) + f(2x - y) + f(2y) + f(x + y) - f(-x + y) - f(x - y) - f(-x - y) = 3f(x) + 3f(y) in a fuzzy normed space.

Poguntke, Detlev
Published in
Advances in Pure and Applied Mathematics

It was one of great successes of Kirillov's orbit method to see that the unitary dual of an exponential Lie group is in bijective correspondence with the orbit space associated with the linear dual of the Lie algebra of the group in question. To show that this correspondence is an homeomorphism turned out to be unexpectedly difficult. Only in 1994 ...

Zeglami, Driss Fadli, Brahim Kabbaj, Samir
Published in
Advances in Pure and Applied Mathematics

Let G be a locally compact group and let μ be a regular, compactly supported, complex-valued Borel measure on G. In the present paper, we determine the continuous solutions f,g : G → ℂ of the functional equation ∫G {f(xyt) + f(xy -1t)}dμ(t) = 2g(x)f(y), x,y ∈ G, in terms of characters, additive maps and matrix elements of irreducible, two-dimension...

Ben Saïd, Salem Boussen, Asma Sifi, Mohamed
Published in
Advances in Pure and Applied Mathematics

We prove various versions of uncertainty principles for a certain Fourier transform ℱA. Here, A is a Chébli function (that is, a Sturm–Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of Gelfand–Shilov type, of Morgan type, of Hardy type, and of Cowling–Price t...

Bonami, Aline Nana, Cyrille
Published in
Advances in Pure and Applied Mathematics

This is essentially a survey on tube domains over irreducible symmetric cones or their bounded realizations. It includes the fact that in rank 2 these inequalities have now been proved for the whole range of possible exponents p, due to recent work of Bourgain and Demeter. We also discuss Lp estimates with loss for the bounded domains and conclude ...