Best Proximity Point Theorems for p-Proximalα-η-β-Quasi Contractions in Metric Spaces with w0-Distance

In this paper,we propose a new class of non-self mappings called p-proximalα-η-β-quasi contraction,and introduce the concepts ofα-proximal admissible mapping with respect toηand(α,d)regular mapping with respect toη.Based on these new notions,we study the existence and uniqueness of best proximity point for this kind of new contractions in metric spaces with w;-distance and obtain a new theorem,which generalize and complement the results in[Ayari,M.I.et al.Fixed Point Theory Appl.,2017,2017:16]and[Ayari,M.I.et al.Fixed Point Theory Appl.,2019,2019:7].We give an example to show the validity of our main result.Moreover,we obtain several consequences concerning about best proximity point and common fixed point results for two mappings,and we present an application of a corollary to discuss the solutions to a class of systems of Volterra type integral equations.     

完备的$\nu$-广义度量空间上的不动点定理[英文]

本文对度量空间中$C$类函数的压缩映射进行推广. 在完备的$\nu$-广义度量空间上, 利用构造迭代序列的方法, 证明了关于($\psi$,$\phi$)-类型压缩映射的不动点定理. 并且证明了广义的$F$类型压缩和广义$\theta$类型压缩映射.     

Banach空间中非线性$\Phi$-伪压缩映象不动点的迭代逼近

本文研究了非线性拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象的不动点的迭代逼近问题.研究结果表明: 在任意实的Banach空间$E$中,拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象$T$~($T$不必连续)的具误差的Ishikawa与Mann迭代序列强收敛于$T$的唯一不动点.所得结果不但改进和推广了最近一些文献的相关结果,而且也改进了定理的证明方法.     

集值映射$\epsilon$-超次梯度的性质及应用[英文]

本文讨论集值映射$\epsilon$-超次梯度的性质，建立$\epsilon$-超次梯度意义下的Moreau-Rockafellar定理.作为应用， 借助$\epsilon$-超次梯度分别得到集值优化取得$\epsilon$-超有效元的充分和必要条件.     

$\mathbb{C}^n$中单位球上$\rho$次抛物星形映射的一些估计

主要研究了$\mathbb{C}^n$中单位球$B^{n}$上$\rho \ (\rho \in [0,1))$次抛物星形映射的一些几何性质, 给出了该映射类的增长定理和掩盖定理, 及其齐次展开式中二次项的一些估计.     

代数$\Omega$-范畴的等价范畴

本文基于$\Omega$-范畴研究了(连续) $\mathcal{I}$-余万备$\Omega$-范畴的一些性质. 我们给出了双完备$\Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$\mathcal{I}$-余万备$\Omega$-范畴都是双完备$\Omega$-范畴. 得到了代数$\Omega$-范畴范畴等价于双完备$\Omega$-范畴.     

一类新型$\alpha$-可容许映射及相关公共不动点定理

本文定义一种向量版本的三角型 $\alpha$-可容许映射, 在没有利用锥的正规性条件下, 得到赋值Banach代数的锥度量空间中的带有三角型 $\alpha$-admissible映射的几种压缩映射的公共不动点定理, 所给出的结论进一步改进了前人的一些结果.     

$\mathbb{C}^n$中一类星形映射子族的增长定理及推广的Roper-Suffridge算子

在有界星形圆形域上定义了一个新的星形映射子族, 它包含了$\alpha$阶星形映射族和$\alpha$阶强星形映射族作为两个特殊子类. 给出了此类星形映射子族的增长定理和掩盖定理. 另外, 还证明了Reinhardt域$\Omega_{n,p_{2},\cdots,p_{n}}$上此星形映射子族在Roper-Suffridge算子 \begin{align*} F(z)=\Big(f(z_{1}),\Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{2}}(f'(z_{1}))^{\gamma_{2}}z_{2},\cdots, \Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{n}}(f'(z_{1}))^{\gamma_{n}}z_{n}\Big)' \end{align*} 作用下保持不变, 其中 $\Omega_{n,p_{2},\cdots,p_{n}}=\{z\in {\mathbb{C}}^{n}:|z_1|^2+|z_2|^{p_2}+\cdots + |z_n|^{p_n}<1\}$, $p_{j}\geq1$, $\beta_{j}\in$ $[0, 1]$, $\gamma_{j}\in[0, \frac{1}{p_{j}}]$满足$\beta_{j}+\gamma_{j}\leq1$, 所取的单值解析分支使得 $\big({\frac{f(z_{1})}{z_{1}}}\big)^{\beta_{j}}\big|_{z_{1}=0}=1$, $(f'(z_{1}))^{\gamma_{j}}\mid_{{z_{1}=0}}=1$, $j=2,\cdots,n$. 这些结果不仅包含了许多已有的结果, 而且得到了新的结论.     

$\varOmega$-凸集的组合与结构性质[英文]

本文研究$\varOmega$-凸集的组合性质和结构性质. 在一定条件下, 证明关于$\varOmega$-凸集的Randon型定理, Helly型定理. Caratheodory型定理以及Minkowski型定理, 并举例说明对一般的$\varOmega$-凸集这些定理不一定成立. 文中所得结果是关于凸集的这些类型定理的推广, 同时也为有关$\varOmega$-凸函数的研究提供了理论工具.     

赋$\beta$-范空间中的最佳逼近问题

本文讨论赋$\beta$-范空间中的最佳逼近问题.以[1]引进的共轭锥为工具,借助[2]中关于$\beta$-次半范的Hahn-Banach延拓定理,第二节给出赋$\beta$-范空间的闭子空间中最佳逼近元的特征,第三节得到赋$\beta$-范空间中任何凸子集或子空间均为半Chebyshev集的充要条件是空间本身严格凸,文章最后证明了严格凸的赋$\beta$-范空间中任何有限维子空间都是Chebyshev集.     

Convergence theorems of a hybrid algorithm for equilibrium problems

In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of common fixed points of two hemi-relatively non-expansive mappings and the set of solutions of an equilibrium problem by the CQ hybrid method in Banach spaces. Our results improve and extend the corresponding results announced by Cheng and Tian [Y. Cheng, M. Tian, Strong convergence theorem by monotone hybrid algorithm for equilibrium problems, hemi-relatively nonexpansive mappings and maximal monotone operators, Fixed Point Theory Appl. 2008 (2008) 12 pages, doi:10.1155/2008/617248], Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively non-expansive mappings, Fixed Point Theory Appl. (2008) doi:10.1155/2008/528476] and some others.     

$$\varvec{\varphi }$$-admissibility results via extended simulation functions

We introduce the class of extended simulation functions, which is more large than the class of simulation functions, recently introduced in (Khojasteh et al. Filomat 29(6):1189–1194, 2015). We obtain a \(\varphi \)-admissibility result involving extended simulation functions, for a new class of mappings \(T: X\rightarrow X\), with respect to a lower semi-continuous function \(\varphi : X\rightarrow [0,\infty )\), where X is a set equipped with a certain metric d. The main theorem in this paper generalizes a recent \(\varphi \)-admissibility result obtained in (Karap?nar et al. Fixed Point Theory Appl 2015:152, 2015), and many other related results.     

Approximate Lie $\ast$-Derivations on $\rho$-complete Convex Modular algebras

In this paper, we obtain generalized Hyers--Ulam stability results of a $(m,n)$-Cauchy-Jensen functional equation associated with approximate Lie $*$-derivations on $\rho$-complete convex modular $*$-algebras $\chi_\rho$ with $\Delta_\mu$-condition on the convex modular $\rho$.     

A note on the reducibility of automorphisms of the Klein curve and the -invariant of mapping tori

We give a characterization for the reducibility of automorphisms of the genus 3 Klein curve in terms of the -invariant of finite order mapping tori.

     

Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of ω-distance in relational metric spaces. Thus we generalize the recent results of Senapati and Dey [J. Fixed Point Theory Appl. 19, 2945-2961 (2017)] and many other important results relevant to this literature. In order to revel the usefulness of such investigations, an application to first order periodic boundary value problem are given. Moreover, we furnish a non-trivial example to demonstrate the validity of our generalization over previous existing results.     

η-INVARIANT AND CHERN-SIMONS CURRENT

The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined ηinvariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.     

强双三角子空间格代数上的$\phi$-导子

Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C-derivations and C-derivations at zero point on Alg：D are generalized Ф-derivations.     

Common tripled fixed point results in cone metric type spaces

In this paper, we prove some common tripled fixed point and tripled coincidence point results for contractive conditions in a cone metric type space. Our results extend, unify and generalize well-known results in the literature, in particular the recent results of Aydi et al. (Fixed Point Theory Appl 2012:134, 2012). Some examples are also presented to validate our obtained results and new concepts.