Pointwise limits of subsequences and -sets
Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces
Pointwise regularity associated with function spaces and multifractal analysis
The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces are constructed, leading to a notion of pointwise regularity with respect to E; the case corresponds to the usual Hölder regularity, and...
Pólya Operators I: Total Positivity.
Pólya Operators II: Complete Concavity.
Polynomial approximation and twenty years later.
Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus
Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs...
Polynomial inequalities for non-commuting operators.
Polynomial inequalities, functional spaces and best approximation on the real semiaxis with Laguerre weights.
Polynomial inequalities on general subsets of
Polynomial interpolation and asymptotic representations for zeta functions [Book]
Polynomial selections and separation by polynomials
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
Polynomial set-valued functions
The aim of this paper is to give a necessary and sufficient condition for a set-valued function to be a polynomial s.v. function of order at most 2.
Polynomial two-point expansions.
Polynomials and convex sequence inequalities.
Polynomials and degrees of maps in real normed algebras
Let be the algebra of quaternions or octonions . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial has a root in . As a consequence, the Jacobian determinant is always non-negative in . Moreover, using the idea of the topological degree we show that a regular polynomial over has also a root in . Finally, utilizing multiplication () in , we prove various results on the topological degree of products...
Polynomials, sign patterns and Descartes' rule of signs
By Descartes’ rule of signs, a real degree polynomial with all nonvanishing coefficients with sign changes and sign preservations in the sequence of its coefficients () has positive and negative roots, where and . For , for every possible choice of the sequence of signs of coefficients of (called sign pattern) and for every pair satisfying these conditions there exists a polynomial with exactly positive and exactly negative roots (all of them simple). For this is not...
Porosity and continuous, nowhere differentiable functions
Porosity, derived numbers and knot points of typical continuous functions
Positive derivatives and increasing functions.