Ayissi, Raoul Domingo Etoua, Remy Magloire
Published in
Advances in Pure and Applied Mathematics

In 2005, Briani and Rampazzo [4], using the results of [10, 12, 13, 14], gave a density approach to Hamilton–Jacobi equations with t-measurable Hamiltonians. In this paper we firstly give more details and do more investigation on viscosity solutions for Hamilton–Jacobi equations. Then we show, using an important result of [4], the existence and uni...

Banerjee, Abhijit Chakraborty, Bikash
Published in
Advances in Pure and Applied Mathematics

In this paper we shall find some sufficient conditions for a uniqueness polynomial to be a strong uniqueness polynomial, as this type of problem was never investigated by researchers earlier. We also exhibit some examples to substantiate our theorems.

Naduvath, Sudev
Published in
Advances in Pure and Applied Mathematics

Let X be a non-empty ground set and 𝒫 ( X ) ${\mathscr{P}(X)}$ be its power set. A set-labeling (or a set-valuation) of a graph G is an injective set-valued function f : V ( G ) → 𝒫 ( X ) ${f\colon\hskip-0.853583ptV(G)\hskip-0.853583pt\to\hskip-0.853583pt\mathscr{P}(% X)}$ such that the induced function f ∗ : E ( G ) → 𝒫 ( X ) ${f^{\ast}\...

Irfan, Syed Shakaib Khan, Mohammad F. Farajzadeh, Ali P. Shafie, Allahkaram
Published in
Advances in Pure and Applied Mathematics

In this paper, we introduce a new class of resolvent operator, the η-proximal operator, and discuss some of its properties. We consider a new generalized variational-like inclusion problem involving relaxed monotone operators in Hilbert space and construct a new iterative algorithm for proving the existence of the solutions of our problem. Our resu...

Trimèche, Khalifa
Published in
Advances in Pure and Applied Mathematics

We consider the hypergeometric translation operators associated to the Cherednik operators and the Heckman–Opdam theory on ℝ d ${\mathbb{R}^{d}}$ introduced by the author in [6]. Under some conditions on the root system and the multiplicity function, we prove in this paper that these operators are positivity preserving and allow positive integral r...

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

Ayoujil, Abdesslem Ourraoui, Anass
Published in
Advances in Pure and Applied Mathematics

In this paper, we study a transmission problem given by a system of two nonlinear equations of p ( x ) ${p(x)}$ -Kirchhoff type with nonstandard growth conditions. Using a variational approach, we establish at least one nontrivial weak solution.

Barhoumi, Najoua
Published in
Advances in Pure and Applied Mathematics

Our aim is to investigate through a special family of Laguerre–Hahn forms of class one verifying the three-term recurrence relation with β n = ( - 1 ) n β 0 ${\beta_{n}=(-1)^{n}\beta_{0}}$ , n ≥ 0 ${n\geq 0}$ , by using quadratic decomposition. The corresponding characteristic elements of the three-term recurrence relation are given explicitly.

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

In a previous paper we introduced a family of differential-reflection operators Λ A , ε ${\Lambda_{A,\varepsilon}}$ acting on smooth functions defined on ℝ ${{\mathbb{R}}}$ , where the spectral problem for the operators Λ A , ε ${\Lambda_{A,\varepsilon}}$ has been studied. Here A is a Sturm–Liouville function with additional hypotheses and - 1 ≤ ε ...

Vashisht, Lalit K. Deepshikha,
Published in
Advances in Pure and Applied Mathematics

Two discrete frames { ϕ i } i ∈ I ${\{\phi_{i}\}_{i\in I}}$ and { ψ i } i ∈ I ${\{\psi_{i}\}_{i\in I}}$ for a separable Hilbert space ℍ ${\mathbb{H}}$ are said to be woven if there are universal positive constants A and B such that for every subset σ ⊂ I ${\sigma\subset I}$ , the family { ϕ i } i ∈ σ ∪ { ψ i } i ∈ σ c ${\{\phi_{i}\}_{i\in\sigma}\cu...