In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansio...In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rec tangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function...In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function.展开更多
Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is...Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method. In order to verify the method, several numerical examples are carried out. The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.展开更多
Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods fo...Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods for computing finite-part integrals.展开更多
The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve ...The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.展开更多
A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
We consider a normalized family F of analytic functions f, whose common domain is the complement of a closed ray in the complex plane. If f(z) is real when z is real and the range of f does not intersect the nonpositi...We consider a normalized family F of analytic functions f, whose common domain is the complement of a closed ray in the complex plane. If f(z) is real when z is real and the range of f does not intersect the nonpositive real axis, then f can be reproduced by integrating the biquadratic kernel against a probability measure u(t) . It is shown that while this integral representation does not characterize the family F, it applies to a large class of functions, including a collection of functions which multiply the Hardy space Hp into itself.展开更多
Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator i...Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.展开更多
文摘In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rec tangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
文摘In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
基金The Key Scientific and Technological Innovation Team Project(2014KCT-15)in Shaanxi Province
文摘In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function.
基金The project supported by the Foundation of the Science Research of the State Education Commission of the People's Republic of China
文摘Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method. In order to verify the method, several numerical examples are carried out. The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.
文摘Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods for computing finite-part integrals.
文摘The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
文摘We consider a normalized family F of analytic functions f, whose common domain is the complement of a closed ray in the complex plane. If f(z) is real when z is real and the range of f does not intersect the nonpositive real axis, then f can be reproduced by integrating the biquadratic kernel against a probability measure u(t) . It is shown that while this integral representation does not characterize the family F, it applies to a large class of functions, including a collection of functions which multiply the Hardy space Hp into itself.
文摘Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.
