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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2005年第2期309卷 583-590页

作者： Ben-El-Mechaiekh, H Chebbi, S Florenzano, M Ecole Polytech Tunisie LEGI Tunis 2078 Tunisia Amer Univ Sharjah Dept Math Stat & Comp Sci Sharjah U Arab Emirates Univ Paris 01 MSE CERMSEM F-75647 Paris France

We present in this paper a generalized version of the celebrated Knaster-Kuratowski-Mazurkiewicz-Fan's principle on the intersection of a family of closed sets subject to a classical geometric condition and a weakened compactness condition. The fixed point formulation of this generalized principle extends the Browder-Fan fixed point theorem to set-valued maps of non-compact convex subsets of topological vector spaces. (C) 2004 Elsevier Inc. All rights reserved.

关键词： fixed-point theory COMPLEMENTARITY-PROBLEMS THEOREMS

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Static Posterior Inference of Bayesian Probabilistic Programming via Polynomial Solving

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PROCEEDINGS OF THE ACM ON PROGRAMMING LANGUAGES-PACMPL 2024年第PLDI期8卷 1361-1386页

作者： Wang, Peixin Yang, Tengshun Fu, Hongfei Li, Guanyan Ong, C. -H. Luke Nanyang Technol Univ Singapore Singapore Chinese Acad Sci Inst Software Beijing Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Shanghai Jiao Tong Univ Shanghai Peoples R China Univ Oxford Oxford England

In Bayesian probabilistic programming, a central problem is to estimate the normalised posterior distribution (NPD) of a probabilistic program with conditioning via score (a.k.a. observe) statements. Most previous approaches address this problem by Markov Chain Monte Carlo and variational inference, and therefore could not generate guaranteed outcomes within a finite time limit. Moreover, existing methods for exact inference either impose syntactic restrictions or cannot guarantee successful inference in general. In this work, we propose a novel automated approach to derive guaranteed bounds for NPD via polynomial solving. We first establish a fixed-point theorem for the wide class of score-at-end Bayesian probabilistic programs that terminate almost-surely and have a single bounded score statement at program termination. Then, we propose a multiplicative variant of Optional Stopping Theorem (OST) to address score-recursive Bayesian programs where score statements with weights greater than one could appear inside a loop. Bayesian nonparametric models, enjoying a renaissance in statistics and machine learning, can be represented by score-recursive Bayesian programs and are difficult to handle due to an integrability issue. Finally, we use polynomial solving to implement our fixed-point theorem and OST variant. To improve the accuracy of the polynomial solving, we further propose a truncation operation and the synthesis of multiple bounds over various program inputs. Our approach can handle Bayesian probabilistic programs with unbounded while loops and continuous distributions with infinite supports. Experiments over a wide range of benchmarks show that compared with the most relevant approach (Beutner et al., PLDI 2022) for guaranteed NPD analysis via recursion unrolling, our approach is more time efficient and derives comparable or even tighter NPD bounds. Furthermore, our approach can handle score-recursive programs which previous approaches could not.

关键词： probabilistic programming Bayesian inference static analysis martingales fixed-point theory posterior distributions

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Viscosity approximation methods for solving fixed-point problems and split common fixed-point problems

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JOURNAL OF fixed point theory AND APPLICATIONS 2017年第2期19卷 1481-1499页

作者： Duong Viet Thong Natl Econ Univ Fac Econ Math 207 Giai Phong St Hanoi Vietnam

In this paper, we introduce the strong convergence theorem for the viscosity approximation methods for solving the split common fixed-point problem in Hilbert spaces. As a consequence, we obtain strong convergence theorems for split variational inequality problems for Lipschitz continuous and monotone operators and split common null point problems for maximal monotone operators. Our results improve and extend the corresponding results announced by many others.

关键词： fixed-point theory Split common fixed-point problem Split feasibility problem Split variational inequality problem Split null point problem

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Dynamics of Caputo fractional-order SIRV model:The effects of imperfect vaccination on disease transmission

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International Journal of Biomathematics 2024年第4期17卷 267-285页

作者： Auwal Abdullahi Mohd Hafiz Mohd Department of Mathematics and Computer Science Federal University Kashere Nigeria School of Mathematical Sciences Universiti Sains Malaysia 11800 USMPulau PinangMalaysia

Though vaccination protects individuals against many infectious diseases,such protection does not always last forever since a few vaccinated individuals could lose their lifelong immunity and eventually become *** study,therefore,determines the effects of imperfect vaccination and memory index on the spread of diseases through the Caputo fractional-order SIRV(Susceptible-Infected-Recovered-Vaccinated)epidemic *** properties of the new model including the conditions for the existence of a unique solution determined through the fixed-point theory and the conditions for the existence of a positive solution of the model obtained via the Mittag-Leffler function along with the Laplace transformation-are thoroughly ***,our simulation results report that an increase in the imperfect vaccination force increases the population of infected *** the memory effect,the higher“memory”the epidemic system has of past states(which corresponds to decreasing values of fractionalorder parameter),the greater the peaks and magnitudes of infection shaping the epidemiological system dynamics.

关键词： Vaccination model fractional-order model Caputo fractional-order derivative Mittag-Leffer function fixed-point theory

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Parameter Optimization for a Novel Inerter-based Dynamic Vibration Absorber with Negative Stiffness

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JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 2022年第2期29卷 280-295页

作者： Li, Jing Gu, Xueqing Zhu, Shaotao Yu, Changlong Yang, Xiaodong Beijing Univ Technol Fac Sci Interdisciplinary Res Inst Beijing 100124 Peoples R China Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China Beijing Univ Technol Fac Mat & Mfg Beijing 100124 Peoples R China

A novel dynamic vibration absorber(DVA) model with negative stiffness and inerter-mass is presented and analytically studied in this paper. The research shows there are still two fixed points independent of the absorber damping in the amplitude frequency curve of the primary system when the system contains negative stiffness and inerter-mass. The optimum frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal negative stiffness ratio. Accordingly, the best working range of inerter is determined and optimal negative stiffness ratio and approximate optimal damping ratio are also obtained. At last the control performance of the presented DVA is compared with three existing typical DVAs. The comparison results in harmonic and random excitation show that the presented DVA could not only reduce the peak value of the amplitude-frequency curve of the primary system significantly, but also broaden the efficient frequency range of vibration mitigation.

关键词： Dynamic vibration absorber Negative stiffness Inerter-mass fixed-point theory Parameters optimization

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Existence analysis on a coupled multiorder system of FBVPs involving integro-differential conditions

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2022年第1期2022卷 1-16页

作者： Samadi, Ayub Mohammadi, Jamshid Mursaleen, M. Islamic Azad Univ Dept Math Miyaneh Branch Miyaneh Iran Islamic Azad Univ Dept Elect Engn Miyaneh Branch Miyaneh Iran China Med Univ Taiwan China Med Univ Hosp Dept Med Res Taichung Taiwan Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

In this research study, we investigate the existence and uniqueness of solutions for a coupled multiorder system of fractional differential equations involving coupled integro-differential boundary conditions in the Riemann-Liouville setting. The presented results are obtained via classical Banach principle along with Leray-Schauder and Krasnosel'skii's fixed-point theorems. Examples are included to support the effectiveness of the obtained results.

关键词： Boundary value problems Riemann-Liouville fractional derivative Caputo fractional derivative Systems of fractional differential equation fixed-point theory

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Existence of intransitive equilibria in nonconvex economies

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SET-VALUED ANALYSIS 1995年第4期3卷 307-337页

作者： Gourdel, P UNIV PARIS 01 ECOLE POLYTECHCERMSEMLAB ECONOMETRIEF-75634 PARIS 13FRANCE

We consider a general equilibrium model of an economy with increasing returns to scale or more general types of nonconvexity and without ordered preferences. Firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other firms. We suppose, moreover, that the pricing rule of the firms verifies a condition of weak bounded losses. This includes the case of profit maximizing, average cost pricing and marginal (cost) pricing, thanks to a transformation used by Bonnisseau. The tastes of the consumers may depend both on other consumptions and on the prices This paper reports a general existence result in this model which extends the results of Bonnisseau and Comet.

关键词： general equilibrium theory increasing returns marginal pricing rule Clarke cone fixed-point theory

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Periodic solutions of neutral functional differential equations

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JOURNAL OF DIFFERENTIAL EQUATIONS 2023年第1期350卷 89-123页

作者： Afonso, S. M. Bonotto, E. M. da Silva, M. R. Univ Estadual Paulista UNESP Inst Geociencias & Ciencias Exatas Campus Rio ClaroAve 24-A1515 BR-13506900 Rio Claro SP Brazil Univ Sao Paulo Inst Ciencias Matemat & Comp Campus Sao CarlosCaixa Postal 668 BR-13560970 Sao Carlos SP Brazil

We provide sufficient conditions for the existence and uniqueness of periodic solutions of a general class of neutral functional differential equations of type d dt (x(t) - A(t, xt)) = f (t, xt) defined almost everywhere in R. As a consequence, we study the existence and uniqueness of periodic solutions for this class of NFDEs under impulse perturbations. Examples are presented to illustrate the developed theory.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Neutral functional differential equations Periodic solutions Impulsive neutral functional differential equations fixed-point theory

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The Schauder and Krasnoselskii fixed-point Theorems on a Frechet Space

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2018年第3期15卷 1-7页

作者： El Arwadi, Toufic Cherif, Mohamed Amine Beirut Arab Univ Dept Math & Comp Sci Fac Sci POB 11-5020 Beirut Lebanon Univ Sfax Fac Sci Sfax Dept Math Route Soukra Km 3-5BP 11713000 Sfax Tunisia

In this manuscript, we study some fixed-point theorems of the Schauder and Krasnoselskii type in a Frechet topological vector space E. We prove a fixed-point theorem which is for every weakly compact map from a closed bounded convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has a fixed point. Using our results, we will establish a new version of the Krasnoselskii fixed-point theorem.

关键词： fixed-point theory Frechet topological vector space Krasnoselskii fixed-point theorems Schauder fixed-point theorems Dunford-Pettis property

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Fully nonlinear fourth-order equations with functional boundary conditions

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2008年第1期340卷 239-251页

作者： Cabada, A. Minhos, F. M. Univ Santiago de Compostela Fac Matemat Dept Anal Matemat Santiago De Compostela 15782 Galicia Spain CIMA UE Dept Matemat P-700671 Evora Portugal

The aim of this paper consists in to give sufficient conditions to ensure the existence and location of the solutions of a nonlinear fully fourth-order equation with functional boundary conditions. The arguments make use of the upper and lower solutions method, a phi-Laplacian operator and a fixed point theorem. An application of the beam theory to a nonlinear continuous model of the human spine allows to estimate its deformation under some loading forces. (c) 2007 Elsevier Inc. All rights reserved.

关键词： fourth-order functional problems Nagumo-type condition lower and upper solutions fixed-point theory beam equation human spine continuous model

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