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.
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
In this note, we discuss a well-known inequality which attracts considerable interest recently. We first obtain a full version of the inequality, then we give a concise and elementary proof which reveals its very esse...In this note, we discuss a well-known inequality which attracts considerable interest recently. We first obtain a full version of the inequality, then we give a concise and elementary proof which reveals its very essential. This naturally leads us to some more general extensions of it. Meanwhile, we point out some mistakes in the existing literature concerning the inequality.展开更多
In this paper, we introduce a new mapping in connection to a recent generalization of Hadamard＇s inequalities for convex functions which gives a continuous scale of refinements of the mentioned inequalities. Some app...In this paper, we introduce a new mapping in connection to a recent generalization of Hadamard＇s inequalities for convex functions which gives a continuous scale of refinements of the mentioned inequalities. Some applications are also mentioned.展开更多
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.
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.
文摘In this note, we discuss a well-known inequality which attracts considerable interest recently. We first obtain a full version of the inequality, then we give a concise and elementary proof which reveals its very essential. This naturally leads us to some more general extensions of it. Meanwhile, we point out some mistakes in the existing literature concerning the inequality.
文摘In this paper, we introduce a new mapping in connection to a recent generalization of Hadamard＇s inequalities for convex functions which gives a continuous scale of refinements of the mentioned inequalities. Some applications are also mentioned.
