Articles

Relaxed alternating CQ algorithms for the split equality problem in Hilbert spaces

In this paper, we are concerned with the split equality problem (SEP) in Hilbert spaces. By converting it to a coupled fixed-point equation, we propose a new algorithm for solving the SEP. Whenever the convex ...

Authors: Hai Yu and Fenghui Wang

Improved McClelland and Koolen–Moulton bounds for distance energy of a graph

Let G be a graph with n vertices and m edges. The term energy of a graph G was introduced by I. Gutman in chemistry due to its relevance to the total π-electron energy of a carbon compound. An analogous energy

Authors: G. Sridhara, M. R. Rajesh Kanna, R. Pradeep Kumar and D. Soner Nandappa

Equivalent property of a half-discrete Hilbert’s inequality with parameters

By using the weight functions and the idea of introducing parameters, a half-discrete Hilbert inequality with a nonhomogeneous kernel and its equivalent form are given. The equivalent statements of the constan...

Authors: Zhenxiao Huang and Bicheng Yang

Certain new bounds considering the weighted Simpson-like type inequality and applications

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some app...

Authors: Chun-Yan Luo, Ting-Song Du, Mehmet Kunt and Yao Zhang

Shrinkage estimation of non-negative mean vector with unknown covariance under balance loss

Parameter estimation in multivariate analysis is important, particularly when parameter space is restricted. Among different methods, the shrinkage estimation is of interest. In this article we consider the pr...

Authors: Hamid Karamikabir, Mahmoud Afshari and Mohammad Arashi

The refinement and generalization of Hardy’s inequality in Sobolev space

In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend t...

Authors: Xiaomin Xue and Fushan Li

A variational inequality of Kirchhoff-type in \(\mathbb{R}^{N}\)

Authors: Jiabin Zuo, Tianqing An and Wei Liu

A class of fourth-order parabolic equation with logarithmic nonlinearity

In this paper, we study a class of fourth-order parabolic equation with the logarithmic nonlinearity. By using the potential well method, we obtain the existence of the unique global weak solution. In addition...

Authors: Pingping Li and Changchun Liu

Extragradient subgradient methods for solving bilevel equilibrium problems

In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lip...

Authors: Tadchai Yuying, Bui Van Dinh, Do Sang Kim and Somyot Plubtieng

Renormalized self-intersection local time of bifractional Brownian motion

Authors: Zhenlong Chen, Liheng Sang and Xiaozhen Hao

Bonnesen-style inequalities on surfaces of constant curvature

Authors: Min Chang

Sufficient and necessary conditions of complete convergence for asymptotically negatively associated random variables

In this investigation, some sufficient and necessary conditions of the complete convergence for weighted sums of asymptotically negatively associated (ANA, in short) random variables are presented without the ...

Authors: Haiwu Huang, Qingxia Zhang and Xiongtao Wu

A generalized Dunkl type modifications of Phillips operators

The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of Szász type operators known as Phillips operators. To achieve the r...

Authors: M. Nasiruzzaman and Nadeem Rao

Sharp two-parameter bounds for the identric mean

Authors: Omran Kouba

Implicit symmetric and symplectic exponentially fitted modified Runge–Kutta–Nyström methods for solving oscillatory problems

Symplectic exponentially fitted RK and RKN methods have been extensively studied by many researchers. Due to their good property, they have been applied to many problems such as pendulum, Morse oscillator, har...

Authors: Bing Zhen Chen and Wen Juan Zhai

A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions

In this article, we first develop a semi-discretized Crank–Nicolson format about time for the two-dimensional non-stationary Stokes equations about vorticity–stream functions and analyze the existence, uniquen...

Authors: Yanjie Zhou, Zhendong Luo and Fei Teng

Uniform asymptotics for ruin probabilities in a two-dimensional nonstandard renewal risk model with stochastic returns

In this paper, we consider a two-dimensional nonstandard renewal risk model with stochastic returns, in which the two lines of claim sizes form a sequence of independent and identically distributed random vect...

Authors: Yinghua Dong and Dingcheng Wang

Refinement of Jensen’s inequality and estimation of f- and Rényi divergence via Montgomery identity

Jensen’s inequality is important for obtaining inequalities for divergence between probability distribution. By applying a refinement of Jensen’s inequality (Horváth et al. in Math. Inequal. Appl. 14:777–791, 201...

Authors: Khuram Ali Khan, Tasadduq Niaz, Ðilda Pec̆arić and Josip Pec̆arić

The viscosity solutions approach to swing options pricing under a regime-switching mean-reverting model

In this paper, we study the valuation of swing options on electricity markets with local volume and refraction time constraints, under the setting that the dynamic of the underlying spot price is a 2-state reg...

Authors: Lingjie Shao, Kaili Xiang and Yang Song

Central limit theorems for sub-linear expectation under the Lindeberg condition

In this paper, we investigate the central limit theorems for sub-linear expectation for a sequence of independent random variables without assumption of identical distribution. We first give a bound on the dis...

Authors: Cheng Hu

General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions

In this paper, we introduce two general iterative methods (one implicit method and one explicit method) for finding a solution of a general system of variational inequalities (GSVI) with the constraints of fin...

Authors: Qian-Wen Wang, Jin-Lin Guan, Lu-Chuan Ceng and Bing Hu

Further results on robust stability for uncertain neutral systems with distributed delay

This paper studies the problem of robust stability for uncertain neutral systems with distributed delay. By utilizing the incorporation of a new integral inequality technique and a novel Lyapunov–Krasovskii fu...

Authors: Tao Wu, Lianglin Xiong, Jinde Cao and Xinzhi Liu

New approximation inequalities for circular functions

Authors: Ling Zhu and Marija Nenezić

New existence results for nonlinear delayed differential systems at resonance

Authors: Ruipeng Chen and Xiaoya Li

Strong convergence theorem for split monotone variational inclusion with constraints of variational inequalities and fixed point problems

In this paper, inspired by Jitsupa et al. (J. Comput. Appl. Math. 318:293–306, 2017), we propose a general iterative scheme for finding a solution of a split monotone variational inclusion with the constraints of...

Authors: Jin-Lin Guan, Lu-Chuan Ceng and Bing Hu

Quantitative unique continuation for the heat equations with inverse square potential

In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of ...

Authors: Guojie Zheng, Keqiang Li and Yuanyuan Zhang

Hermite–Hadamard inequalities and their applications

New Hermite–Hadamard type inequalities are established. Some corresponding examples are also discussed in detail.

Authors: Marcela V. Mihai, Muhammad Uzair Awan, Muhammad Aslam Noor, Jong Kyu Kim and Khalida Inayat Noor

Blow-up analysis for a periodic two-component μ-Hunter–Saxton system

The two-component μ-Hunter–Saxton system is considered in the spatially periodic setting. Firstly, two wave-breaking criteria are derived by employing the transport equation theory and the localization analysis m...

Authors: Yunxi Guo and Tingjian Xiong

Weighted version of Hermite–Hadamard type inequalities for geometrically quasi-convex functions and their applications

This paper presents new weighted Hermite–Hadamard type inequalities for a new class of convex functions which are known as geometrically quasi-convex functions. Some applications of these results to special me...

Authors: Sofian Obeidat and Muhammad Amer Latif

Jensen–Steffensen inequality for strongly convex functions

The Jensen inequality for convex functions holds under the assumption that all of the included weights are nonnegative. If we allow some of the weights to be negative, such an inequality is called the Jensen–S...

Authors: M. Klaričić Bakula

Boundedness of a class of rough maximal functions

In this work, we obtain appropriate sharp bounds for a certain class of maximal operators along surfaces of revolution with kernels in

Authors: Mohammed Ali and Omar Al-mohammed

Hardy-type inequalities within fractional derivatives without singular kernel

In this manuscript, we developed the Hardy-type inequality within the Caputo–Fabrizio fractional derivative. We presented some illustrative examples to confirm our work.

Authors: Yasemin Başcı and Dumitru Baleanu

Norm inequalities related to the Heinz means

Authors: Fugen Gao and Xuedi Ma

New Jensen and Hermite–Hadamard type inequalities for h-convex interval-valued functions

In this paper, we introduce the h-convex concept for interval-valued functions. By using the h-convex concept, we present new Jensen and Hermite–Hadamard type inequalities for interval-valued functions. Our inequ...

Authors: Dafang Zhao, Tianqing An, Guoju Ye and Wei Liu

Applications of a q-Salagean type operator on multivalent functions

Authors: Saqib Hussain, Shahid Khan, Muhammad Asad Zaighum and Maslina Darus

A new generalization of Halanay-type inequality and its applications

In this paper, in order to study the dissipativity of nonlinear neutral functional differential equations, a generalization of the Halanay inequality is given. We apply this generalized Halanay inequality to a...

Authors: Haiyang Wen, Shi Shu and Liping Wen

Globally proper efficiency of set-valued optimization and vector variational inequality involving the generalized contingent epiderivative

In this paper, firstly, a new property of the cone subpreinvex set-valued map involving the generalized contingent epiderivative is obtained. As an application of this property, a sufficient optimality conditi...

Authors: Wang Chen and Zhiang Zhou

RETRACTED ARTICLE: On stability analysis for generalized Minty variational-hemivariational inequality in reflexive Banach spaces

The stability for a class of generalized Minty variational-hemivariational inequalities has been considered in reflexive Banach spaces. We demonstrate the equivalent characterizations of the generalized Minty ...

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

Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian

Authors: Meng Qu and Liu Yang

On multipliers of matrix domains

Authors: Gholamreza Talebi

Large deviation principle for the mean reflected stochastic differential equation with jumps

In this paper, we establish a large deviation principle for a mean reflected stochastic differential equation driven by both Brownian motion and Poisson random measure. The weak convergence method plays an imp...

Authors: Yumeng Li

Generalized nonlinear weakly singular retarded integral inequalities with maxima and their applications

This paper deals with a generalized nonlinear weakly singular retarded Wendroff-type integral inequality with maxima of an unknown function of two variables. The key is that a technique of monotonization witho...

Authors: Yong Yan, Derong Zhou and Jianglin Zhao

Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay

This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the fre...

Authors: Tengyu Ma and Longsuo Li

Some limit properties for a hidden inhomogeneous Markov chain

This paper presents a general strong limit theorem for delayed sum of functions of random variables for a hidden time inhomogeneous Markov chain (HTIMC), and as corollaries, some strong laws of large numbers f...

Authors: Yun Dong, Fang-qing Ding and Qi-feng Yao

AE solutions to two-sided interval linear systems over max-plus algebra

This paper introduces a concept of AE solutions to two-sided interval max-plus linear systems, a rather general concept which includes many known concepts of solutions to interval systems, in particular, weak,...

Authors: Lihua Wang, Wei Li and Haohao Li

Higher-order error bound for the difference of two functions

Error bounds play an important role in the research of mathematical programming. Using some techniques of nonsmooth analysis, we establish some results on the existence of higher-order error bounds for differe...

Authors: Hui Huang and Mengxue Xia

Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces

In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of t...

Authors: Jinhua Zhu, Jinfang Tang and Shih-sen Chang

Bellman–Steffensen type inequalities

In this paper some Bellman–Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen’s inequality, nonnormalized versions of Steffensen’s ...

Authors: Julije Jakšetić, Josip Pečarić and Ksenija Smoljak Kalamir

A Dunkl type generalization of Szász operators via post-quantum calculus

The object of this paper to construct Dunkl type Szász operators via post-quantum calculus. We obtain some approximation results for these new operators and compute convergence of the operators by using the mo...

Authors: Abdullah Alotaibi, Md. Nasiruzzaman and M. Mursaleen

Lyapunov-type inequalities for an anti-periodic fractional boundary value problem involving ψ-Caputo fractional derivative

Authors: Bessem Samet and Hassen Aydi