A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fra...A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.展开更多
Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamar...Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.展开更多
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
Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special ca...Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.展开更多
An absolute value equation is established for linear combinations of two operators.When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in litera...An absolute value equation is established for linear combinations of two operators.When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained.Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2]and [3].展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11801342)the Natural Science Foundation of Shaanxi Province(Grant No.2023-JC-YB-043).
文摘A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.
基金Supported by the key scientific and technological innovation team project in shaanxi province(2014KCT-15)the Foundations of Shaanxi Educational committee(NO.18Jk0152)
文摘Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.
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 NSF(11801342) of Chinathe Foundation(18JK0116) of Shaanxi Educational Committee
文摘Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.
基金Supported by the Key Scientific and Technological Innovation Team Project in Shaanxi Province(2014KCT-15)
文摘An absolute value equation is established for linear combinations of two operators.When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained.Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2]and [3].
