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
Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the n...Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the number of sides or surfaces separated by edges, can vary in a non-trivial manner depending on the degree of twisting during the revolution. We use the term “Kideas” to specifically denote these polysurfacic tori, and we represent the number of sides (referred to as “facets”) of the original polygon followed by a point, while the number of facets from which the torus is twisted during its revolution is indicated. We then explore the use of concave regular polygons to generate Kideas. We finally give acceleration for the algorithm for calculating the set of prime numbers.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.
文摘Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the number of sides or surfaces separated by edges, can vary in a non-trivial manner depending on the degree of twisting during the revolution. We use the term “Kideas” to specifically denote these polysurfacic tori, and we represent the number of sides (referred to as “facets”) of the original polygon followed by a point, while the number of facets from which the torus is twisted during its revolution is indicated. We then explore the use of concave regular polygons to generate Kideas. We finally give acceleration for the algorithm for calculating the set of prime numbers.
