Articles

Convergence analysis of a variable metric forward–backward splitting algorithm with applications

The forward–backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and an inverse strongly monotone operator. In this paper...

Authors: Fuying Cui, Yuchao Tang and Chuanxi Zhu

The interpolation of Young’s inequality using dyadics

In this article we interpolate Young’s inequality using a delicate treatment of dyadics. Although there are other simple methods to prove these results, we present this new approach hoping to reveal more of th...

Authors: Mohammad Sababheh and Abdelrahman Yousef

A general slicing inequality for measures of convex bodies

Authors: Yufeng Yu

Rank-one perturbation bounds for singular values of arbitrary matrices

Rank-one perturbation of arbitrary matrices has many practical applications. In this paper, based on the relationship between the singular values and the eigenvalues, we discuss singular value variations and p...

Authors: Lei Zhu, Xiaofei Peng and Hao Liu

A new extragradient algorithm for split equilibrium problems and fixed point problems

In this paper, we present a new extragradient algorithm for approximating a solution of the split equilibrium problems and split fixed point problems. The strong convergence theorems are proved in the framewor...

Authors: Narin Petrot, Mohsen Rabbani, Manatchanok Khonchaliew and Vahid Dadashi

The method of lower and upper solutions for the cantilever beam equations with fully nonlinear terms

Authors: Yongxiang Li and Yabing Gao

Generalized fractional integral inequalities of Hermite–Hadamard type for \({(\alpha,m)}\)-convex functions

Authors: Feng Qi, Pshtiwan Othman Mohammed, Jen-Chih Yao and Yong-Hong Yao

On weighted cumulative past (residual) inaccuracy for record values

In this paper, we propose the weighted cumulative past (residual) inaccuracy for record values. For this concept, we obtain some properties and characterization results such as relationships with other reliabi...

Authors: Safieh Daneshi, Ahmad Nezakati and Saeid Tahmasebi

On extreme points and product properties of a new subclass of p-harmonic functions

In this paper, we introduce a new subclass of p-harmonic functions and investigate the univalence and sense-preserving, extreme points, distortion bounds, convex combination, neighborhoods of mappings belonging t...

Authors: Shu-Hai Li, Huo Tang and Xiao-Meng Niu

The convergence of \((p,q)\)-Bernstein operators for the Cauchy kernel with a pole via divided difference

Authors: Faisal Khan, Mohd Saif, Aiman Mukheimer and M. Mursaleen

On a new class of convex functions and integral inequalities

The aim of this paper is to introduce a new extension of convexity called σ-convexity. We show that the class of σ-convex functions includes several other classes of convex functions. Some new integral inequaliti...

Authors: Shanhe Wu, Muhammad Uzair Awan, Muhammad Aslam Noor, Khalida Inayat Noor and Sabah Iftikhar

Improved LMI-based stability conditions for a competitive Lotka–Volterra system with time-varying delays

This paper is concerned with the local asymptotic stability problem for a competitive Lotka–Volterra system with time-varying delays. By constructing the novel augmented Lyapunov–Krasovskii functionals and usi...

Authors: Rui Dong, Lei Chen and Yonggang Chen

A note on degenerate Bernstein polynomials

Recently, degenerate Bernstein polynomials have been introduced by Kim and Kim. In this paper, we investigate some properties and identities for the degenerate Bernstein polynomials associated with special num...

Authors: Taekyun Kim, Dae San Kim, Gwan-Woo Jang and Jongkyum Kwon

A fundamental proof of convergence of alternating direction method of multipliers for weakly convex optimization

The convergence of the alternating direction method of multipliers (ADMMs) algorithm to convex/nonconvex combinational optimization has been well established in the literature. Due to the extensive application...

Authors: Tao Zhang and Zhengwei Shen

A new discrete Hilbert-type inequality involving partial sums

In this paper, we derive a new discrete Hilbert-type inequality involving partial sums. Moreover, we show that the constant on the right-hand side of this inequality is the best possible. As an application, we...

Authors: Vandanjav Adiyasuren, Tserendorj Batbold and Laith Emil Azar

Estimates for the commutators of operator \(V^{\alpha }\nabla (-\Delta +V)^{-\beta }\)

Authors: Yue Hu and Yueshan Wang

An inexact proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth optimization problems

In this paper, we propose an inexact version of proximal gradient algorithm with extrapolation for solving a class of nonconvex nonsmooth optimization problems. Specifically, the subproblem in proximal gradien...

Authors: Zehui Jia, Zhongming Wu and Xiaomei Dong

Efficiency of orthogonal super greedy algorithm under the restricted isometry property

We investigate the efficiency of orthogonal super greedy algorithm (OSGA) for sparse recovery and approximation under the restricted isometry property (RIP). We first show that under the RIP conditions of the ...

Authors: Xiujie Wei and Peixin Ye

Equivalent properties of a Mulholland-type inequality with a best possible constant factor and parameters

By means of the weight coefficients, using the idea of introduced parameters and the techniques of real analysis, a Mulholland-type inequality with a homogeneous kernel and an equivalent form are provided. Som...

Authors: Hongmin Mo and Bicheng Yang

Fuglede–Putnam type theorems for \((p,k)\)-quasihyponormal operators via hyponormal operators

Authors: Jiang-Tao Yuan and Cai-Hong Wang

Boundedness and essential norm of an integral-type operator on a Hilbert–Bergman-type spaces

Authors: Stevo Stević and Zhi-Jie Jiang

Asymptotic tail probability of weighted infinite sum of conditionally dependent and consistently varying tailed random variables

This paper investigates the asymptotic behavior of the tail probability of a weighted infinite sum of random variables with consistently varying tails under two conditional dependence structures. The obtained ...

Authors: Qingwu Gao, Xijun Liu and Chunhong Chai

Statistical inference for the new INAR(2) models with random coefficient

In this paper, we investigate a random coefficient INAR(2) process which may model the number of traded stocks, the number of infected people, the number of birds in some area, etc. We show that this process i...

Authors: Xu Wang

Extensions of inequalities for sector matrices

In this note, we first prove an inequality for sector matrices. This complements a result due to Kittaneh and Sakkijha (Linear Multilinear Algebra, 2018,

Authors: Song Lin and Xiaohui Fu

A unified approach to fractal Hilbert-type inequalities

In the present study we provide a unified treatment of fractal Hilbert-type inequalities. Our main result is a pair of equivalent fractal Hilbert-type inequalities including a general kernel and weight functio...

Authors: Tserendorj Batbold, Mario Krnić and Predrag Vuković

Generalized strong vector quasi-equilibrium problems with variable ordering structure

In this paper, two kinds of generalized strong vector quasi-equilibrium problems with variable ordering structure are considered by using the concept of cosmically upper continuity rather than upper semi-conti...

Authors: Jia-Yu Mao, San-hua Wang and Jin-xia Huang

Some reverse mean inequalities for operators and matrices

In this paper, we present some new reverse arithmetic–geometric mean inequalities for operators and matrices due to Lin (Stud. Math. 215:187–194, 2013). Among other inequalities, we prove that if

Authors: Chaojun Yang, Yaxin Gao and Fangyan Lu

Theorems of complete convergence and complete integral convergence for END random variables under sub-linear expectations

The goal of this paper is to build complete convergence and complete integral convergence for END sequences of random variables under sub-linear expectation space. By using the Markov inequality, we extend som...

Authors: Ziwei Liang and Qunying Wu

Several properties of hypergeometric Bernoulli numbers

In this paper, we give several characteristics of hypergeometric Bernoulli numbers, including several identities for hypergeometric Bernoulli numbers which the convergents of the continued fraction expansion o...

Authors: Miho Aoki, Takao Komatsu and Gopal Krishna Panda

Approximation properties of generalized Baskakov–Schurer–Szasz–Stancu operators preserving \(e^{-2ax}, a>0\)

Authors: Melek Sofyalıoğlu and Kadir Kanat

Some fractional integral inequalities of type Hermite–Hadamard through convexity

In the present article, the authors have established some Hermite–Hadamard type integral inequalities via Riemann–Liouville fractional integrals that generalize Hermite–Hadamard type inequalities and a few oth...

Authors: Shahid Qaisar, Jamshed Nasir, Saad Ihsan Butt, Asma Asma, Farooq Ahmad, Muhammad Iqbal and Sajjad Hussain

More results on integral inequalities for strongly generalized \(( \phi,h,s )\)-preinvex functions

The main goal of this research is to introduce a new form of generalized Hermite–Hadamard and Simpson type inequalities utilizing Riemann–Liouville fractional integral by a new class of preinvex functions whic...

Authors: Shahid Qaisar, Jamshed Nasir, Saad Ihsan Butt and Sabir Hussain

Growth of meromorphic solutions of linear difference equations without dominating coefficients

Authors: Dong-Mei Wei and Zhi-Gang Huang

\((p,q)\)-gamma operators which preserve \(x^{2}\)

Authors: Wen-Tao Cheng, Wen-Hui Zhang and Qing-Bo Cai

Random sampling and approximation of signals with bounded derivatives

Approximation of analog signals from noisy samples is a fundamental, but nevertheless difficult problem. This paper addresses the problem of approximating functions in ...

Authors: Jianbin Yang and Xinzhu Tao

Adaptive wavelet estimations for the derivative of a density in GARCH-type model

Authors: Kaikai Cao and Jingyi Wei

Hermite–Hadamard’s trapezoid and mid-point type inequalities on a disk

Authors: M. Rostamian Delavar, S. S. Dragomir and M. De La Sen

Nontrivial solutions for an integral boundary value problem involving Riemann–Liouville fractional derivatives

In this paper using topological degree we study the existence of nontrivial solutions for a fractional differential equation involving integral boundary conditions. Here, the nonlinear term may be sign-changin...

Authors: Zhengqing Fu, Shikun Bai, Donal O’Regan and Jiafa Xu

Approximation on parametric extension of Baskakov–Durrmeyer operators on weighted spaces

In the present manuscript, we define a non-negative parametric variant of Baskakov–Durrmeyer operators to study the convergence of Lebesgue measurable functions and introduce these as α-Baskakov–Durrmeyer operato...

Authors: Md Nasiruzzaman, Nadeem Rao, Samar Wazir and Ravi Kumar

Positive periodic solution for p-Laplacian neutral damped Duffing equation with strong singularities of attractive and repulsive type

Authors: Shaowen Yao and Xiaozhong Zhang

A Gronwall inequality via the generalized proportional fractional derivative with applications

In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional frac...

Authors: Jehad Alzabut, Thabet Abdeljawad, Fahd Jarad and Weerawat Sudsutad

Iterated commutators of multilinear Calderón–Zygmund maximal operators on some function spaces

Authors: Zengyan Si and Pu Zhang

On Shannon and Zipf–Mandelbrot entropies and related results

In this paper, we present some interesting results related to the bounds of the Shannon and the Zipf–Mandelbrot entropies. Further, we define linear functionals and present their properties. We also construct ...

Authors: Sadia Khalid, Ðilda Pečarić and Josip Pečarić

Lyapunov-type inequalities for sequential fractional boundary value problems using Hilfer’s fractional derivative

This paper is devoted to studying the Lyapunov-type inequality for sequential Hilfer fractional boundary value problems. We first provide some properties of Hilfer fractional derivative, and then establish Lya...

Authors: Wei Zhang and Wenbin Liu

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

Minkowski’s inequality for the AB-fractional integral operator

Recently, AB-fractional calculus has been introduced by Atangana and Baleanu and attracted a large number of scientists in different scientific fields for the exploration of diverse topics. An interesting aspe...

Authors: Hasib Khan, Thabet Abdeljawad, Cemil Tunç, Abdulwasea Alkhazzan and Aziz Khan

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