Articles

Extensions and demonstrations of Hölder’s inequality

In this paper, we present some new extensions of Hölder’s inequality and give a condition under which the equality holds. We also show that many existing inequalities related to the Hölder inequality are parti...

Authors: Fei Yan and Qin Gao

Retraction Note: On stability analysis for generalized Minty variational-hemivariational inequality in reflexive Banach spaces

The authors have retracted this article [1] because it significantly overlaps with the previously published article by Zhong and Huang [2]. All authors agree to this retraction.

Authors: Lu-Chuan Ceng, Ravi P. Agarwal, Jen-Chih Yao and Yonghong Yao

Certain geometric properties of Mittag-Leffler functions

Authors: Saddaf Noreen, Mohsan Raza and Sarfraz Nawaz Malik

Inequalities between the inverse hyperbolic tangent and the inverse sine and the analogue for corresponding functions

In this paper, we obtain some new inequalities which reveal the further relationship between the inverse tangent function arctanx and the inverse hyperbolic sine function sinh⁻¹x. At the same time, we give the an...

Authors: Ling Zhu and Branko Malešević

Hermite–Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications

In this paper, we introduce the notion of exponentially p-convex function and exponentially s-convex function in the second sense. We establish several Hermite–Hadamard type inequalities for exponentially p-conve...

Authors: Naila Mehreen and Matloob Anwar

A Hilbert-type integral inequality under configuring free power and its applications

By using the method of weight function, the technique of real analysis, and the theory of special functions, a multi-parameter Hilbert-type integral inequality and its equivalent form are established, and thei...

Authors: Qiong Liu

Convergence properties of the maximum partial sums for moving average process under \(\rho^{-}\)-mixing assumption

Authors: Mingzhu Song and Quanxin Zhu

The forward–backward splitting methods for variational inequalities and minimization problems in Banach spaces

This paper is concerned with the study of a class of forward–backward splitting methods based on Lyapunov distance for variational inequalities and convex minimization problem in Banach spaces.

Authors: Wei-Bo Guan and Wen Song

A certain subclass of meromorphically q-starlike functions associated with the Janowski functions

In this paper, the authors introduce a new subclass of meromorphic q-starlike functions which are associated with the Janowski functions. A characterization of meromorphically q-starlike functions associated with...

Authors: Shahid Mahmood, Qazi Zahoor Ahmad, H. M. Srivastava, Nazar Khan, Bilal Khan and Muhammad Tahir

A sharp reverse Bonnesen-style inequality and generalization

We investigate the isoperimetric deficit of the oval domain in the Euclidean plane. Via the kinematic formulae of Poincaré and Blaschke, and Blaschke’s rolling theorem, we obtain a sharp reverse Bonnesen-style...

Authors: Pengfu Wang

Asymptotic estimates for n-width of fuzzy numbers

n-widths in approximation theory characterize how well one can approximate a subset by some “good” subsets of a normed linear space. Especially, n-widths of sets of ...

Authors: Yong J. Han, Liu Liang and Guang G. Chen

Log-Minkowski inequalities for the \(L_{p}\)-mixed quermassintegrals

Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies. Recently, Stancu proved the log-Minkowski inequality for mixed volumes;...

Authors: Chao Li and Weidong Wang

V-singular values of rectangular tensors and their applications

The positive definiteness of rectangular tensors has wide applications in solid mechanics and quantum physics. By modifying the existing definition of singular value for rectangular tensors, some V-singular va...

Authors: Jun He, Yanmin Liu, Guangjun Xu and Gang Liu

A semi-smoothing augmented Lagrange multiplier algorithm for low-rank Toeplitz matrix completion

The smoothing augmented Lagrange multiplier (SALM) algorithm is a generalization of the augmented Lagrange multiplier algorithm for completing a Toeplitz matrix, which saves computational cost of the singular ...

Authors: Ruiping Wen, Shuzhen Li and Yonghong Duan

Lower bound of four-dimensional Hausdorff matrices

Authors: Gholamreza Talebi

The Minkowski inequality involving generalized k-fractional conformable integral

In the research paper, the authors exploit the definition of a new class of fractional integral operators, recently proposed by Jarad et al. (Adv. Differ. Equ. 2017:247, 2017), to define a new class of generalize...

Authors: Shahid Mubeen, Siddra Habib and Muhammad Nawaz Naeem

Linear convergence of the relaxed gradient projection algorithm for solving the split equality problems in Hilbert spaces

In this paper, we consider the relaxed gradient projection algorithm to solve the split equality problem in Hilbert spaces, and we investigate its linear convergence. In particular, we use the concept of the b...

Authors: Tingting Tian, Luoyi Shi and Rudong Chen

Iteration complexity of generalized complementarity problems

The goal of this paper is to discuss iteration complexity of two projection type methods for solving generalized complementarity problems and establish their worst-case sub-linear convergence rates measured by...

Authors: Salahuddin and Meshari Alesemi

\((h-m)\)-convex functions and associated fractional Hadamard and Fejér–Hadamard inequalities via an extended generalized Mittag-Leffler function

Authors: Shin Min Kang, Ghulam Farid, Waqas Nazeer and Sajid Mehmood

Some algorithms for classes of split feasibility problems involving paramonotone equilibria and convex optimization

In this paper, we first introduce a new algorithm which involves projecting each iteration to solve a split feasibility problem with paramonotone equilibria and using unconstrained convex optimization. The str...

Authors: Q. L. Dong, X. H. Li, D. Kitkuan, Y. J. Cho and P. Kumam

Tensor product dual frames

To construct dual frames with good structure for a given frame is a fundamental problem in the theory of frames. The tensor product duals of tensor product frames can provide a rank-one decomposition of bounde...

Authors: Ya-Hui Wang and Yun-Zhang Li

On the error estimation and T-stability of the Ishikawa iteration for strongly demicontractive mappings

In this paper, some new formula of error estimations of Ishikawa iteration and some strong convergence theorems of strongly demicontractive mappings are first obtained. And then, convergence speeds and error e...

Authors: Chao Wang, Xueli Li and Pengkun Huang

On the weak convergence for solving semistrictly quasi-monotone variational inequality problems

In this paper, we study the approximation problem of solutions for the semistrictly quasi-monotone variational inequalities in infinite-dimensional Hilbert spaces. We prove that the iterative sequence generate...

Authors: S. S. Chang, Salahuddin, L. Wang and M. Liu

Improvements of bounds for the Sándor–Yang means

In the article, we provide new bounds for two Sándor–Yang means in terms of the arithmetic and contraharmonic means. Our results are the improvements of the previously known results.

Authors: Wei-Mao Qian, Hui-Zuo Xu and Yu-Ming Chu

On positive solutions for some second-order three-point boundary value problems with convection term

In this paper, a fixed point theorem in a cone and some inequalities of the associated Green’s function are applied to obtain the existence of positive solutions of second-order three-point boundary value prob...

Authors: Yongfang Wei, Zhanbing Bai and Sujing Sun

General viscosity approximation methods for quasi-nonexpansive mappings with applications

The purpose of this paper is to introduce and study the general viscosity approximation methods for quasi-nonexpansive mappings in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions,...

Authors: Xindong Liu, Zili Chen and Yun Xiao

Generalized multivalued Khan-type \((\psi ,\phi )\)-contractions in complete metric spaces

Authors: Yun Xiao, Zhijian Qiu and Xindong Liu

Characterizing the R-duality of g-frames

In this paper, we define the g-Riesz-dual of a given special operator-valued sequence with respect to g-orthonormal bases for a separable Hilbert space. We demonstrate that the g-R-dual keeps some synchronous ...

Authors: Liang Li and Pengtong Li

Modified HS conjugate gradient method for solving generalized absolute value equations

Authors: Ya Li and Shouqiang Du

A note on certain integrals along polynomial compound curves

In this paper we consider a singular integral operator and a parametric Marcinkiewicz integral operator with rough kernel. These operators have singularity along sets of the form curves ...

Authors: Feng Liu and Pu Zhang

Notes on the uniqueness of meromorphic functions concerning differential polynomials

This paper is devoted to the uniqueness problem on meromorphic functions whose differential polynomials share one nonzero finite constant. We improve some previous results and answer two open problems posed by...

Authors: Fengrong Zhang and Linlin Wu

p-adic singular integrals and their commutators in generalized Morrey spaces

Authors: Hui X. Mo, Zhe Han, Liu Yang and Xiao J. Wang

Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors

In this paper, we establish the strong consistency and complete consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions....

Authors: Qihui He

Blow-up criteria for the 3D Bénard system in Besov spaces

This paper studies the regularity criteria of weak solutions for Bénard fluid flows in three dimensions. When the velocity field and the temperature belong to some critical Besov spaces on ...

Authors: Liangliang Ma and Lei Zhang

Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series

The main purpose and motivation of this work is to investigate and provide some new identities, inequalities and relations for combinatorial numbers and polynomials, and for Peters type polynomials with the he...

Authors: Yilmaz Simsek and Ji Suk So

Difference-based M-estimator of generalized semiparametric model with NSD errors

Authors: Fangning Fu, Zhen Zeng and Xiangdong Liu

Analysis of a stochastic predator–prey population model with Allee effect and jumps

This paper is concerned with a stochastic predator–prey model with Allee effect and Lévy noise. First, by the comparison theorem of stochastic differential equations, we prove that the model has a unique globa...

Authors: Rong Liu and Guirong Liu

Inclusion relations for certain families of integral operators associated with conic regions

In this work, we introduce certain subclasses of analytic functions involving the integral operators that generalize the class of uniformly starlike, convex, and close-to-convex functions with respect to symme...

Authors: Shahid Mahmood, Imran Khan, Hari Mohan Srivastava and Sarfraz Nawaz Malik

Majorization theorems for strongly convex functions

In the article, we present several majorization theorems for strongly convex functions and give their applications in inequality theory. The given results are the improvement and generalization of the earlier ...

Authors: Syed Zaheer Ullah, Muhammad Adil Khan and Yu-Ming Chu

Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

In this paper, we study the Schur m-power convexity of the generalized geometric Bonferroni mean involving three parameters. Our result provides a unified generalization to the work that was done recently by Shi ...

Authors: Shan-He Wu and Yu-Ming Chu

A generalized nonlinear Picone identity for the p-biharmonic operator and its applications

A generalized nonlinear Picone identity for the p-biharmonic operator is established in this paper. As applications, a Sturmian comparison principle to the p-biharmonic equation with singular term, a Liouville’s ...

Authors: Tingfu Feng

Oscillation of higher-order differential equations with distributed delay

Authors: O. Bazighifan, E. M. Elabbasy and O. Moaaz

Some inequalities involving the polygamma functions

Authors: Lichun Liang, Bin Zhao and Aibing Li

Approximating trigonometric functions by using exponential inequalities

In this paper, some exponential inequalities are derived from the inequalities containing trigonometric functions. Numerical examples show that one can achieve much tighter bounds than those of prevailing meth...

Authors: Xiao-Diao Chen, Junyi Ma and Yixin Li

Hyperbolic curve flows in the plane

In this paper, we investigate the evolution of a strictly convex closed planar curve driven by a hyperbolic normal flow. The asymptotical behavior of the evolving curves has also been shown if the velocity of the...

Authors: Zhe Zhou, Chuan-Xi Wu and Jing Mao

Inequalities for Katugampola conformable partial derivatives

In the paper, we introduce two concepts of Katugampola conformable partial derivatives and α-conformable integrals. As applications, we establish Opial type inequalities for Katugampola conformable partial deriva...

Authors: Chang-Jian Zhao and Wing-Sum Cheung

On eigenvalue inequalities of a matrix whose graph is bipartite

We consider the set of real zero diagonal symmetric matrices whose underlying graph, if not told otherwise, is bipartite. Then we establish relations between the eigenvalues of such matrices and those arising ...

Authors: Abdullah Alazemi, Milica Anđelić and Slobodan K. Simić

Optimality conditions for interval-valued univex programming

We introduce concepts of interval-valued univex mappings, consider optimization conditions for interval-valued univex functions for the constrained interval-valued minimization problem, and show examples for t...

Authors: Lifeng Li, Jianke Zhang and Chang Zhou

Gibbs phenomenon for p-ary subdivision schemes

When a Fourier series is used to approximate a function with a jump discontinuity, the Gibbs phenomenon always exists. This similar phenomenon exists for wavelets expansions. Based on the Gibbs phenomenon of a...

Authors: Jie Zhou, Hongchan Zheng and Baoxing Zhang

Stochastic ordering of Pólya random variables and monotonicity of the Bernstein–Stancu operator for a negative parameter

In the present paper, we prove that the probabilities of the Pólya urn distribution (with negative replacement) satisfy a monotonicity property similar to that of the binomial distribution. As a consequence, w...

Authors: Florenţa Tripşa and Nicolae R. Pascu