We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H...We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].展开更多
In this paper, we study the relations between meromorphic functions and their derivatives with one shared values, and obtain a concrete expression of meromorphic functions of zero order that share one value CM with th...In this paper, we study the relations between meromorphic functions and their derivatives with one shared values, and obtain a concrete expression of meromorphic functions of zero order that share one value CM with their derivatives by a new method. Our main result is the supplementary of a related result due to Li and Yi(Li X M, Yi H X. Uniqueness of meromorphic functions sharing a meromorphic function of a small order with their derivatives. Ann. Polon. Math., 2010, 98(3):201–219).展开更多
In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-Gδ properties,?0-snf-countability and csf-countability are invariants a...In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-Gδ properties,?0-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings. By the relationships between the weak first-countabilities, we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gfcountability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.展开更多
It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are: (1) A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-w...It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are: (1) A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-weak base; (2) Under (CH), every separable space with a σ-point-discrete N_0-weak base has a countable N_0-weak base.展开更多
We show that the completion of a partial metric space can fail be unique,which answers a question on completions of partial metric spaces.In addition,to this paper discusses metrizability around partial metric spaces.
Let E(a;f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δ...Let E(a;f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δnc f(z) satisfy E(1;f)= E(1;Δnc f), E(0;f) E(0;Δnc f) and E(1;f) E(1;Δnc f), then Δnc f(z) f(z). This result improves a more recent theorem due to Gao et al.(Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476- 018-0605-2) by using a simple method.展开更多
Let I 2N be an ideal and let XI = span{χI : I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to p...Let I 2N be an ideal and let XI = span{χI : I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x*oχ(·) : x*∈ p(e)}, where p(x) = lim supn→∞1/n(∑k=1n|x(k)|, and let Iμ = {A N : μ(A) = 0} for all μ = x*oχ(·) ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent.展开更多
The purpose of this paper is to discuss those kinds of statistical convergence, in terms of F , or ideal Z-convergence, which are equivalent to measure convergence defined by a single statistical measure. We prove a n...The purpose of this paper is to discuss those kinds of statistical convergence, in terms of F , or ideal Z-convergence, which are equivalent to measure convergence defined by a single statistical measure. We prove a number of characterizations of a single statistical measure μ-convergence by using properties of its corresponding quotient Banach space l∞/l∞ (Iμ). We also show that the usual sequential convergence is not equivalent to a single measure convergence.展开更多
基金supported by NSF of Fujian Province,China(S0750013),supported by NSF of Fujian Province,China(2008J0190)the Research Foundation of Ningde Normal University(2008J001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].
文摘In this paper, we study the relations between meromorphic functions and their derivatives with one shared values, and obtain a concrete expression of meromorphic functions of zero order that share one value CM with their derivatives by a new method. Our main result is the supplementary of a related result due to Li and Yi(Li X M, Yi H X. Uniqueness of meromorphic functions sharing a meromorphic function of a small order with their derivatives. Ann. Polon. Math., 2010, 98(3):201–219).
基金Supported by the National Natural Science Foundation of China(11801254,11471153)
文摘In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-Gδ properties,?0-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings. By the relationships between the weak first-countabilities, we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gfcountability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.
基金Supported by the National Natural Science Foundation of China (10971185, 11171162, 11201053)China Postdoctoral Science Foundation funded project (20090461093, 201003571)+1 种基金Jiangsu Planned Projects for Teachers Overseas Research FundsTaizhou Teachers College Research Funds
文摘It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are: (1) A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-weak base; (2) Under (CH), every separable space with a σ-point-discrete N_0-weak base has a countable N_0-weak base.
基金This project is supported by the National Natural Science Foundation of China(11801254,61472469,11461005).
文摘We show that the completion of a partial metric space can fail be unique,which answers a question on completions of partial metric spaces.In addition,to this paper discusses metrizability around partial metric spaces.
基金The NSF (11801291) of China,the NSF (2018J01424) of Fujian Province
文摘Let E(a;f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δnc f(z) satisfy E(1;f)= E(1;Δnc f), E(0;f) E(0;Δnc f) and E(1;f) E(1;Δnc f), then Δnc f(z) f(z). This result improves a more recent theorem due to Gao et al.(Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476- 018-0605-2) by using a simple method.
基金supported by Plan Project of Education Department of Fujian Province(Grant No.JA11275)
文摘Let I 2N be an ideal and let XI = span{χI : I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x*oχ(·) : x*∈ p(e)}, where p(x) = lim supn→∞1/n(∑k=1n|x(k)|, and let Iμ = {A N : μ(A) = 0} for all μ = x*oχ(·) ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent.
文摘The purpose of this paper is to discuss those kinds of statistical convergence, in terms of F , or ideal Z-convergence, which are equivalent to measure convergence defined by a single statistical measure. We prove a number of characterizations of a single statistical measure μ-convergence by using properties of its corresponding quotient Banach space l∞/l∞ (Iμ). We also show that the usual sequential convergence is not equivalent to a single measure convergence.