We investigate the best constants for regional fractional $p$-Poincaré inequality and in cylindrical domains. For special case $p=2$, result was already known due to Chowdhury-Csató-Roy-Sk [Study of Poincaré inequalities on unbounded domains, Discrete Contin. Dyn. Syst., 41(6), 2021]. addressed asymptotic behavior first eigenvalue nonlocal Dirichlet $p$-Laplacian problem when domain is becoming...

In a Banach space X the linear difference equation with constant coefficients x n + p = 1 ? … , is Ulam stable if and only roots r k ? of its characteristic do not belong to unit circle. If | > we prove that best this V ? s ? 2 ( ) where are Vandermonde determinants.

Abstract By the use of weight coefficients and techniques real analysis, we establish a new Hardy–Mulholland-type inequality with mixed kernel best possible constant factor in terms hypergeometric function. Equivalent forms, an operator expression norm reverses are also considered.

In this paper, we present improved inapproximability results for three problems : the problem of finding the maximum clique size in a graph, the problem of finding the chromatic number of a graph, and the problem of coloring a graph with a small chromatic number with a small number of colors. Håstad’s celebrated result [13] shows that the maximum clique size in a graph with n vertices is inappr...

Making use of weight coefficients as well real/complex analytic methods, an extension a Hardy–Hilbert-type inequality with best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression the norm, few particular cases are also considered.