Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co...Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.展开更多
In this paper, the so-called（p,Ф）-Carleson measure is introduced and the rela-tionship between vector-valued martingales in the general Campanato spaces Lp,Ф（X） and the （p, Ф）-Carleson measures is investigate...In this paper, the so-called（p,Ф）-Carleson measure is introduced and the rela-tionship between vector-valued martingales in the general Campanato spaces Lp,Ф（X） and the （p, Ф）-Carleson measures is investigated. Specifically, it is proved that for q ∈ [2, ∞）, the measure d# ：-=││ dfk││^qdP dm is a （q, Ф）-Carleson measure on Ω × N for every f ∈ Lq,Ф（X） if and only if X has an equivalent norm which is q-uniformly convex; while for p C （1, 2], the measure dμ ：=││dfk││^pP dm is a （p, Ф）-Carleson measure on Ω ×N implies that f ∈ Lp,Ф（X） if and only if X admits an equivalent norm which is p-uniformly smooth. This result extends an earlier result in the literature from BMO spaces to general Campanato spaces.展开更多
In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a corr...In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.展开更多
We present a statistical distribution of a nanorobot motion inside the blood.This distribution is like the distribution of A and B particles in continuous time random walk scheme inside the fAuid reactive anomalous tr...We present a statistical distribution of a nanorobot motion inside the blood.This distribution is like the distribution of A and B particles in continuous time random walk scheme inside the fAuid reactive anomalous transport with stochastic waiting time depending on the Gaussian distribution and a Gaussian jump length which is detailed in Zhang and Li[J.Stat.Phys,Published Online with doi:10.1007/s10955-018-2185-8,2018].Rather than estimating the length parameter of the jumping distance of the nanorobot,we normalize the Probability Density Function(PDF)and present some reliability properties for this distribution.In addition,we discuss the truncated version of this distribution and its statistical properties,and estimate its length parameter.We use the estimated distance to study the conditions that give a finite expected value of the first meeting time between this nanorobot in the case of nonlinear flow with independent d-dimensional Gaussian jumps and an independent d-dimensional CD4 T Brownian cell in the blood(d-space)to prevent the HIV virus from proliferating within this cell.展开更多
基金Project supported by the Natural Science Foundation of Sichuan Province of China(No.2005A132)
文摘Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
基金supported by National Natural Science Foundation of China(11601267)
文摘In this paper, the so-called（p,Ф）-Carleson measure is introduced and the rela-tionship between vector-valued martingales in the general Campanato spaces Lp,Ф（X） and the （p, Ф）-Carleson measures is investigated. Specifically, it is proved that for q ∈ [2, ∞）, the measure d# ：-=││ dfk││^qdP dm is a （q, Ф）-Carleson measure on Ω × N for every f ∈ Lq,Ф（X） if and only if X has an equivalent norm which is q-uniformly convex; while for p C （1, 2], the measure dμ ：=││dfk││^pP dm is a （p, Ф）-Carleson measure on Ω ×N implies that f ∈ Lp,Ф（X） if and only if X admits an equivalent norm which is p-uniformly smooth. This result extends an earlier result in the literature from BMO spaces to general Campanato spaces.
文摘In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.
基金The authors gratefully acknowledge the Deanship of Scientific Research,Taibah University for the support of this research work,research Group No.60337.
文摘We present a statistical distribution of a nanorobot motion inside the blood.This distribution is like the distribution of A and B particles in continuous time random walk scheme inside the fAuid reactive anomalous transport with stochastic waiting time depending on the Gaussian distribution and a Gaussian jump length which is detailed in Zhang and Li[J.Stat.Phys,Published Online with doi:10.1007/s10955-018-2185-8,2018].Rather than estimating the length parameter of the jumping distance of the nanorobot,we normalize the Probability Density Function(PDF)and present some reliability properties for this distribution.In addition,we discuss the truncated version of this distribution and its statistical properties,and estimate its length parameter.We use the estimated distance to study the conditions that give a finite expected value of the first meeting time between this nanorobot in the case of nonlinear flow with independent d-dimensional Gaussian jumps and an independent d-dimensional CD4 T Brownian cell in the blood(d-space)to prevent the HIV virus from proliferating within this cell.
