On a Generalization of Strongly $η$-Convex Functions via Fractal Sets

A new generalization of the midpoint formula for n-time differentiable mappings which are convex

In this paper, we establish several new inequalities for n- time differentiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality.

利用模拟函数的广义Proinov型压缩映射及其在分形中的应用

Generalized Proinov-type contractions using simulation functions with applications to fractals

本文通过模拟函数推广Proinov型压缩映射，提出Proinov型Z-压缩，证明其在拟度量空间中不动点的存在唯一性，并构建对应迭代函数系统，证明其存在唯一吸引子。

A generalization of Kantorovich operators for convex compact subsets

In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of probability Borel measures. By considering special cases of these parameters for particular convex compact subsets we obtain the classical Kantorovich operators defined in the one-dimensional and multidimensional setting together with several of their wide-ranging generalizations scattered in the literature. We investigate the approximation properties of thes…

Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets

In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in $\mathbb{R}^n$, we generalize the definition of the Poincaré-Steklov operator to $d$-set boundaries, $n-2< d<n$, and give its spectral properties to compare to the spectra of the interior domain and also of a truncated domain, considered as an approximation of the exterior case. The well-posedness of the Robin boundary value problems for the truncated and exterior domains is given in the general framework of $n$-sets. The results are obtained thanks to a generalization of the conti…

离散康托集的分形不确定性原理何时最具不确定性？

When is the fractal uncertainty principle for discrete Cantor sets most uncertain?

该研究给出离散康托集分形不确定性原理达到最不确定指数的充要条件，研究分布式谱对并完成循环群中的分类，还探讨了连续情形下的对应情况。

New generalization of geodesic convex function

As a generalization of geodesic function, this paper introduces the notion of geodesic $ φ_{E} $-convex function. Some properties of $ φ_{E} $-convex function and geodesic $ φ_{E} $-convex function are established. The concepts of geodesic $ φ_{E} $-convex set and $ φ_{E} $-epigraph are equally given. The characterization of geodesic $ φ_{E} $-convex functions in terms of their $ φ_{E} $-epigraphs are also obtained.

生成与 Suzuki 迭代函数系统相关的分形函数

Generating fractal functions associated with Suzuki iterated function systems

本文提出利用 Suzuki 型广义 $φ$-压缩映射构造 $α$-分形插值函数，并通过新德里菠菜价格案例分析及盒维数分析验证其在价格波动预测中的应用价值。

Some Generalization of Hadamard's type Inequalities through Differentiability for s-Convex Function and their Applications

In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral inequalities contributes some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.