In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive ...In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.展开更多
A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators ...A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.展开更多
In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solution...In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.展开更多
The Brouwer fixed-point theorem in topology states that for any continuous mapping <em>f</em> on a compact convex set into itself admits a fixed point, <em>i.e.</em>, a point <em>x</em...The Brouwer fixed-point theorem in topology states that for any continuous mapping <em>f</em> on a compact convex set into itself admits a fixed point, <em>i.e.</em>, a point <em>x</em><sub>0</sub> such that<em> f</em>(<em>x</em><sub>0</sub>) = <em>x</em><sub>0</sub>. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, <em>i.e.</em>, <em>b</em>(<em>r</em><sub>0</sub>) = <em>r</em><sub>0</sub> for the shape function <em>b</em> = <em>b</em>(<em>r</em>). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.展开更多
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearl...Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.展开更多
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam w...By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.展开更多
In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theore...In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.展开更多
Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by ...Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem （RT） and the method of equivalent edge currents （MEC） are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation （KA） method and physical optics （PO） method, respectively. The effects of the backscattering radar cross section （RCS） and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.展开更多
Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner...Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.展开更多
An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict effi...An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.展开更多
In this paper,the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve ...In this paper,the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.展开更多
基金supported by Università degli Studi di Palermo (Local University Project ex 60%)
文摘In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.
文摘A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.
基金supported by ARC grant of Australiasupported by National Natural Sciences Foundations of China (10961016 and 10631030)NSF of Jiangxi(2009GZS0011)
文摘In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.
文摘The Brouwer fixed-point theorem in topology states that for any continuous mapping <em>f</em> on a compact convex set into itself admits a fixed point, <em>i.e.</em>, a point <em>x</em><sub>0</sub> such that<em> f</em>(<em>x</em><sub>0</sub>) = <em>x</em><sub>0</sub>. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, <em>i.e.</em>, <em>b</em>(<em>r</em><sub>0</sub>) = <em>r</em><sub>0</sub> for the shape function <em>b</em> = <em>b</em>(<em>r</em>). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
文摘Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.
文摘By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.
基金supported by the National Natural Science Foundation of China(No.11361064)the project No.174024 of the Ministry of Education,Science and Technological Department of the Republic of Serbia
文摘In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60971067)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070701010)
文摘Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem （RT） and the method of equivalent edge currents （MEC） are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation （KA） method and physical optics （PO） method, respectively. The effects of the backscattering radar cross section （RCS） and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.
文摘Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.
基金Supported by the National Natural Science Foundation of China(10461007)Supported by the Natural Science Foundation of Jiangxi Province(0611081)
文摘An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.
基金Project Supported by National Natural Science Foundation of China(1 9871 0 4 8) and Natural ScienceFoundation of Shandong Prov
文摘In this paper,the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.
