arXiv subjects

Pinhong Long

Publications and source records attributed to Pinhong Long.

4 recordsLinked to original sources

arXiv2026

Functional inequalities for starlike and convex functions associated with $g$-derivative operator

In this paper we first introduce a new class of derivative operators, termed $g$-derivative operators, which unifies the $q$-derivative, $(p,q)$-derivative and $(\alpha,\beta,\gamma)$-derivative operators, even classical derivative in the literature. Based on this generalized framework, we define two novel function classes, specifically $g$-starlike functions and $g$-convex functions. Further, we employ the subordination principle of analytic functions to conduct the coefficient estimations for such function classes, and subsequently derive the bounds for the corresponding Fekete-Szeg\"{o} inequality, Toeplitz determinants and Hankel determinants.

math.CV↗

arXiv2023

On the symmetric $q$-analog on the bi-univalent functions with respect to symmetric points

Our objective is to usher and investigate the subclass$\widetilde{\mathcal{S^{*}_{\sum}}}^{\eta}_{q}(\mu,\lambda;\phi)$ of the function class $\sum$ of analytic and bi-univalent functions related with the symmetric $q$-derivative operator and the generalized Bernardi integral operator. On the one hand, without the generalized Bernardi integral operator we estimate the second Hankel determinants for the reduced subclasses $\widetilde{\mathcal{S^{*}_{\sum}}}_{q}(\lambda;\phi)$ with respect to symmetric points. On the other hand, we also give the corresponding results of Fekete-Szeg\"{o} functional inequalities and the upper bounds of the coefficients $a_2$ and $a_3$ for these subclasses.

math.CV↗

arXiv2018

A characterization of rough fractional type integral operators and Campanato estimates for their commutators on the variable exponent vanishing generalized Morrey spaces

In this paper, applying some properties of variable exponent analysis, we first dwell on Adams and Spanne type estimates for a class of fractional type integral operators of variable orders, respectively and then, obtain variable exponent generalized Campanato estimates for the corresponding commutators on the vanishing generalized Morrey spaces $VL_{\Pi }^{p\left( \cdot \right) ,w\left( \cdot \right) }\left( E\right) $ with variable exponent $p(\cdot )$ and bounded set $E$

math.AP↗

arXiv2012

Criterions of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schr\"odinger operator in a cone

In the paper we give some criterions for a-minimally thin sets and a-rarefied sets associated with the stationary Schr\"odinger operator at a fixed Martin boundary point or {\infty} with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside a-rarefied set. Finally we illustrate the relation between a-minimally thin set and a-rarefied set in a cone.

math.CA↗