Chaubey, Sudhakar Kumar Yadav, Sunil Kumar
Published in
Advances in Pure and Applied Mathematics

We set a definition of a ( 0 , 2 ) {(0,2)} -type tensor on the generalized Sasakian-space-forms. The necessary and sufficient conditions for W-semisymmetric generalized Sasakian-space forms are studied. Certain results of the Ricci solitons, the Killing vector fields and the closed 1-form on the generalized Sasakian-space-forms are derived. We also...

Adama, Aïssata Feuto, Justin Fofana, Ibrahim
Published in
Advances in Pure and Applied Mathematics

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on ℝ {\mathbb{R}} endowed with a measure which needs not to be doubling.

Sghaier, Mabrouk Zaatra, Mohamed Khlifi, Achraf
Published in
Advances in Pure and Applied Mathematics

We give the system of Laguerre–Freud equations for the recurrence coefficients β n {\beta_{n}} , γ n + 1 {\gamma_{n+1}} , n ≥ 0 {n\geq 0} , of orthogonal polynomials with respect to a D-Laguerre–Hahn form (linear functional) of class one. The system is solved in the case when β 0 = - θ 0 {\beta_{0}=-\theta_{0}} , β n + 1 = θ n - θ n + 1 {\beta_{n+1...

Roger, Claude
Published in
Advances in Pure and Applied Mathematics

We give an introduction to superalgebra, founded on the difference between even (commuting) and odd (anti-commuting) variables. We give a sketch of Graßmann’s work, and show how derivations of those structures induce various superalgebra structures, Lie superalgebras of Cartan type being obtained with even derivations, while odd derivations induce ...

Poria, Anirudha Swain, Jitendriya
Published in
Advances in Pure and Applied Mathematics

Let ℍ {\mathbb{H}} be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the ℍ {\mathbb{H}} -valued Gabor frame operator on ℍ {\mathbb{H}} -valued weighted amalgam spaces W ℍ ( L p , L v q ) {W_{\mathbb{H}}(L^{p},L^{q}_{v})} , 1 ≤ p , q ≤ ∞ {1\leq p,q\leq\infty} . Als...

Ciake Ciake, Fidele Lavenir Takou, Etienne
Published in
Advances in Pure and Applied Mathematics

In this paper, we consider the Cauchy problem for the relativistic Enskog equation with near vacuum data for a hard sphere gas in the Robertson–Walker space-time. We prove an existence and uniqueness result of the global (in time) mild solution in a suitable weighted space. We also study the asymptotic behavior of the solution as well as the L ∞ {L...

Kant, Shashi
Published in
Advances in Pure and Applied Mathematics

In this paper, we investigate the deterministic and stochastic prey-predator system with refuge. The basic local stability results for the deterministic model have been performed. It is found that all the equilibrium points except the positive coexisting equilibrium point of the deterministic model are independent of the prey refuge. The trivial eq...

Muslikh, Mohamad Kilicman, Adem bt Sapar, Siti Hasana bt Bachoklati, Norfifah
Published in
Advances in Pure and Applied Mathematics

In this article, we introduce the notion of “metrically differentiable” for set-valued functions. By using this notion, it is shown that each Lipschitz set-valued function is differentiable almost everywhere. Its relationship to the differentiation in the sense of Hukuhara and its generalizations are also discussed.

Sarkar, Arindam
Published in
Advances in Pure and Applied Mathematics

In this paper, we prove two theorems establishing the uniqueness of the derivatives of meromorphic functions f ( k ) {f^{{(k)}\vphantom{k}}} and g ( k ) {g^{{(k)}\vphantom{k}}} when they share two sets with least cardinalities. Our results improve some existing results of Fang–Lahiri, Banerjee–Bhattacharjee, Banerjee–Mallick and Banerjee–Chakrabort...

Rehman, Nadeem ur
Published in
Advances in Pure and Applied Mathematics

The purpose of this paper is to prove the following result which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let ℒ ( X ) {\mathcal{L}(X)} be the algebra of all bounded linear operators of X into itself and let 𝒜 ( X ) ⊂ ℒ ( X ) {\mathcal{A}(X)\subset\mathcal{L}(X)} be a standard operator algebra. Sup...