The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors...The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors' recent results.展开更多
In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt dom...In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.展开更多
With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a w...With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.展开更多
In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （...In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.展开更多
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is...In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.展开更多
Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finit...Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finite-dim ensionalsubspaces,a stabilization form ulation is pre- sented for the Stokes problem by em ploying nonconform ing elem ents.This form ulation is uni- form ly coercive and notsubject to the Babus ka-Brezzicondition,and the resulted linear algebraic system is positive definitew ith the spectralcondition num berO(h- 2 ). Quasi-optim alerrorbounds are obtained,which is consistentwith the interpola- tion properties ofthe finite elem entsused.展开更多
With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the...With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.展开更多
In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the gen...In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.展开更多
The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschi...The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established.展开更多
The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Th...The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.展开更多
文摘The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors' recent results.
基金supported by the National Natural Science Foundation of China(11001246,11101139)Zhejiang Innovation Project(T200905)
文摘In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.
文摘With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.
基金supported by the research project#144003 of the Serbian Ministry of Science, Technology and Development
文摘In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.
文摘In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.
文摘Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finite-dim ensionalsubspaces,a stabilization form ulation is pre- sented for the Stokes problem by em ploying nonconform ing elem ents.This form ulation is uni- form ly coercive and notsubject to the Babus ka-Brezzicondition,and the resulted linear algebraic system is positive definitew ith the spectralcondition num berO(h- 2 ). Quasi-optim alerrorbounds are obtained,which is consistentwith the interpola- tion properties ofthe finite elem entsused.
基金Supported by the 2007 Year School Grade Plan Item of Inner Mongolia University for Nationalities(MDX2007030)
文摘With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.
文摘In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.
文摘The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established.
文摘The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.
