Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some applica...A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.展开更多
Some new integral and discrete inequalities with power nonlinearity are established. Two recent results of B.G. Pachpatte are improved by some particularcorollaries of our results. Application examples are also indica...Some new integral and discrete inequalities with power nonlinearity are established. Two recent results of B.G. Pachpatte are improved by some particularcorollaries of our results. Application examples are also indicated.展开更多
Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, so...Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.展开更多
The paper studies Sard's problem on construction of optimal quadrature formulas in the space W_(2)^((m,0))by Sobolev's method.This problem consists of two parts:first calculating the norm of the error function...The paper studies Sard's problem on construction of optimal quadrature formulas in the space W_(2)^((m,0))by Sobolev's method.This problem consists of two parts:first calculating the norm of the error functional and then finding the minimum of this norm by coefficients of quadrature formulas.Here the norm of the error functional is calculated with the help of the extremal function.Then using the method of Lagrange multipliers the system of linear equations for coefficients of the optimal quadrature formulas in the space W_(2)^((m,0)) is obtained,moreover the existence and uniqueness of the solution of this system are discussed.Next,the discrete analogue D_(m)(hβ)of the differential operatord^(2m)/dx^(2m)-1 is constructed.Further,Sobolev's method of construction of optimal quadrature formulas in the space W_(2)^((m,0)),which based on the discrete analogue D_(m)(hβ),is described.Next,for m=1 and m=3 the optimal quadrature formulas which are exact to exponential-trigonometric functions are obtained.Finally,at the end of the paper the rate of convergence of the optimal quadrature formulas in the space W_(2)^((3,0))for the cases m=1 and m=3 are presented.展开更多
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
基金the Natural Science Foundation of Guangdong Pronvincial.
文摘A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.
文摘Some new integral and discrete inequalities with power nonlinearity are established. Two recent results of B.G. Pachpatte are improved by some particularcorollaries of our results. Application examples are also indicated.
基金The project is supported in part by the NSF of Guangdong Province (Grnat No. 940651) the SF of Key Discipline of the State Council Office of Overseas Chinese Affairs of China (Grant No.93-93-6)
文摘Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.
基金supported by the “Korea Foundation for Advanced Studies”/“Chey Institute for Advanced Studies” International Scholar Exchange Fellowship for academic year of 2018–2019
文摘The paper studies Sard's problem on construction of optimal quadrature formulas in the space W_(2)^((m,0))by Sobolev's method.This problem consists of two parts:first calculating the norm of the error functional and then finding the minimum of this norm by coefficients of quadrature formulas.Here the norm of the error functional is calculated with the help of the extremal function.Then using the method of Lagrange multipliers the system of linear equations for coefficients of the optimal quadrature formulas in the space W_(2)^((m,0)) is obtained,moreover the existence and uniqueness of the solution of this system are discussed.Next,the discrete analogue D_(m)(hβ)of the differential operatord^(2m)/dx^(2m)-1 is constructed.Further,Sobolev's method of construction of optimal quadrature formulas in the space W_(2)^((m,0)),which based on the discrete analogue D_(m)(hβ),is described.Next,for m=1 and m=3 the optimal quadrature formulas which are exact to exponential-trigonometric functions are obtained.Finally,at the end of the paper the rate of convergence of the optimal quadrature formulas in the space W_(2)^((3,0))for the cases m=1 and m=3 are presented.
