Articles

Approximations to inverse tangent function

In this paper, we present a sharp Shafer-type inequality for the inverse tangent function. Based on the Padé approximation method, we give approximations to the inverse tangent function. Based on the obtained ...

Authors: Quan-Xi Qiao and Chao-Ping Chen

Some new k-Riemann–Liouville fractional integral inequalities associated with the strongly η-quasiconvex functions with modulus \(\mu\geq0\)

A new class of quasiconvexity called strongly η-quasiconvex function was introduced in (Awan et al. in Filomat 31(18):5783–5790, 2017). In this paper, we obtain some new k-Riemann–Liouville fractional integral in...

Authors: Eze R. Nwaeze, Seth Kermausuor and Ana M. Tameru

A two-point-Padé-approximant-based method for bounding some trigonometric functions

Inequalities are frequently used for solving practical engineering problem. There are two key issues of bounding inequalities; one is to find the bounds, and the other is to prove the bounds. This paper takes ...

Authors: Xiao-Diao Chen, Junyi Ma, Jiapei Jin and Yigang Wang

Sobolev’s embedding on time scales

Authors: Naveed Ahmad, Hira Ashraf Baig, Ghaus ur Rahman and M. Shoaib Saleem

Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function

In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev’s inequality for sync...

Authors: Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen and Muhammad Arshad

A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem

In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control proble...

Authors: Lin Li, Zuliang Lu, Wei Zhang, Fei Huang and Yin Yang

A Crank–Nicolson collocation spectral method for the two-dimensional telegraph equations

In this paper, we mainly focus to study the Crank–Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank–Nicolson collocation spectral m...

Authors: Yanjie Zhou and Zhendong Luo

A series of sequences convergent to Euler’s constant

In this paper, using continued fraction, we provide a new quicker sequence convergent to Euler’s constant. We demonstrate the superiority of our new convergent sequences over DeTemple’s sequence, Mortici’s seq...

Authors: Li-Jiang Jia, Bin Ge, Li-Li Liu and Yi Ran

Generalization of the space \(l(p)\) derived by absolute Euler summability and matrix operators

Authors: Fadime Gökçe and Mehmet Ali Sarıgöl

Boundary value problems for hypergenic function vectors

This article mainly studies the boundary value problems for hypergenic function vectors in Clifford analysis. Firstly, some properties of hypergenic quasi-Cauchy type integrals are discussed. Then, by the Scha...

Authors: Guiling Zhang, Chong Li and Yonghong Xie

Smoothing approximation to the lower order exact penalty function for inequality constrained optimization

For inequality constrained optimization problem, we first propose a new smoothing method to the lower order exact penalty function, and then show that an approximate global solution of the original problem can...

Authors: Shujun Lian and Nana Niu

Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of...

Authors: Binayak S. Choudhury, Pranati Maity, Nikhilesh Metiya and Mihai Postolache

Convergence analysis on a modified generalized alternating direction method of multipliers

The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving convex composite minimization problem. The generalized ADMM relaxes both the variables and ...

Authors: Sha Lu and Zengxin Wei

Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers

In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by

Authors: Serkan Araci and Mehmet Acikgoz

On complete convergence and complete moment convergence for weighted sums of \(\rho^{*}\)-mixing random variables

Authors: Pingyan Chen and Soo Hak Sung

Sharp bounds for the Sándor–Yang means in terms of arithmetic and contra-harmonic means

In the article, we provide several sharp upper and lower bounds for two Sándor–Yang means in terms of combinations of arithmetic and contra-harmonic means.

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

Chen’s Ricci inequalities and topological obstructions on null hypersurfaces of a Lorentzian manifold

Given a null hypersurface of a Lorentzian manifold, we isometrically immerse a null hypersurface equipped with the Riemannian metric (induced on it by the rigging) into a Riemannian manifold suitably construct...

Authors: Karimumuryango Ménédore

Extremal functions for Trudinger–Moser inequalities with nonnegative weights

Using blow-up analysis, the author proves the existence of extremal functions for Trudinger–Moser inequalities with nonnegative weights on bounded Euclidean domains or compact Riemannian surfaces. This extends...

Authors: Songbo Hou

The modified proximal point algorithm in Hadamard spaces

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (...

Authors: Shih-sen Chang, Lin Wang, Ching-Feng Wen and Jian Qiang Zhang

Bahadur representations of M-estimators and their applications in general linear models

Authors: Hongchang Hu

The modified split generalized equilibrium problem for quasi-nonexpansive mappings and applications

In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequal...

Authors: Kanyarat Cheawchan and Atid Kangtunyakarn

Gradient projection method with a new step size for the split feasibility problem

In this paper, we introduce an iterative scheme using the gradient projection method with a new step size, which is not depend on the related matrix inverses and the largest eigenvalue (or the spectral radius ...

Authors: Pattanapong Tianchai

Hadamard and Fejér–Hadamard inequalities for extended generalized fractional integrals involving special functions

In this paper we prove the Hadamard and the Fejér–Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function. The extended genera...

Authors: Shin Min Kang, Ghulam Farid, Waqas Nazeer and Bushra Tariq

Optimal bounds for the generalized Euler–Mascheroni constant

We provide several sharp upper and lower bounds for the generalized Euler–Mascheroni constant. As consequences, some previous bounds for the Euler–Mascheroni constant are improved.

Authors: Ti-Ren Huang, Bo-Wen Han, Xiao-Yan Ma and Yu-Ming Chu

Admissibility of simultaneous prediction for actual and average values in finite population

This paper studies the admissibility of simultaneous prediction of actual and average values of the regressand in the generalized linear regression model under the quadratic loss function. Necessary and suffic...

Authors: Chao Bai and Haiqi Li

A new type of Taylor series expansion

We present a variant of the classical integration by parts to introduce a new type of Taylor series expansion and to present some closed forms for integrals involving Jacobi and Laguerre polynomials, which can...

Authors: Mohammad Masjed-Jamei, Zahra Moalemi, Iván Area and Juan J. Nieto

Analysis of stability for stochastic delay integro-differential equations

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square...

Authors: Yu Zhang and Longsuo Li

An extended reverse Hardy–Hilbert’s inequality in the whole plane

Using weight coefficients, a complex integral formula, and Hermite–Hadamard’s inequality, we give an extended reverse Hardy–Hilbert’s inequality in the whole plane with multiparameters and a best possible cons...

Authors: Qiang Chen and Bicheng Yang

A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations

For large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan–Wei–Lu line search technique. It combines the steepest desce...

Authors: Gonglin Yuan and Wujie Hu

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian

The present study is concerned with the following fractional p-Laplacian equation involving a critical Sobolev exponent of Kirchhoff type:

Authors: Liejun Shen

Triple Diamond-Alpha integral and Hölder-type inequalities

In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha...

Authors: Jing-Feng Tian

Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation

Authors: Bingqing Ma and Yongli Dong

A class of derivative-free trust-region methods with interior backtracking technique for nonlinear optimization problems subject to linear inequality constraints

This paper focuses on a class of nonlinear optimization subject to linear inequality constraints with unavailable-derivative objective functions. We propose a derivative-free trust-region methods with interior...

Authors: Jing Gao and Jian Cao

Refined Wirtinger-type integral inequality

Based on the extreme value conditions of a multiple variables function, a new class of Wirtinger-type double integral inequality is established in this paper. The proposed inequality generalizes and refines th...

Authors: Liansheng Zhang and Shuxia Wang

New bounds for the exponential function with cotangent

In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function ...

Authors: Ling Zhu

\(L_{p}\)-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in \(\mathbb{R}^{d}\)

Authors: Mi-Hwa Ko

Genuine modified Bernstein–Durrmeyer operators

The present paper deals with genuine Bernstein–Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre ...

Authors: Syed Abdul Mohiuddine, Tuncer Acar and Mohammed A. Alghamdi

A new smoothing modified three-term conjugate gradient method for \(l_{1}\)-norm minimization problem

Authors: Shouqiang Du and Miao Chen

Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm

The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this pap...

Authors: Yanni Guo and Wei Cui

Lebesgue constants for Chebyshev thresholding greedy algorithms

We investigate the efficiency of Chebyshev Thresholding Greedy Algorithm (CTGA) for an n-term approximation with respect to general bases in a Banach space. We show that the convergence property of CTGA is better...

Authors: Chunfang Shao and Peixin Ye

An alternating linearization bundle method for a class of nonconvex nonsmooth optimization problems

In this paper, we propose an alternating linearization bundle method for minimizing the sum of a nonconvex function and a convex function, both of which are not necessarily differentiable. The nonconvex functi...

Authors: Chunming Tang, Jinman Lv and Jinbao Jian

Existence of weak solutions of stochastic delay differential systems with Schrödinger–Brownian motions

By using new Schrödinger type inequalities appearing in Jiang and Usó (J. Inequal. Appl. 2016:233, 2016), we study the existence of weak solutions of stochastic delay differential systems with Schrödinger–Brownia...

Authors: Jianguo Sun, Liang Kou, Gang Guo, Guodong Zhao and Yong Wang

On Kedlaya-type inequalities for weighted means

Authors: Zsolt Páles and Paweł Pasteczka

Sherman’s and related inequalities with applications in information theory

In this paper we give extensions of Sherman’s inequality considering the class of convex functions of higher order. As particular cases, we get an extended weighted majorization inequality as well as Jensen’s ...

Authors: S. Ivelić Bradanović, N. Latif, Ð. Pečarić and J. Pečarić

A Cauchy type inequality for Möbius operations

In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.

Authors: Keiichi Watanabe

A law of iterated logarithm for the subfractional Brownian motion and an application

Authors: Hongsheng Qi and Litan Yan

On Frame’s inequalities

In this paper, the errors of the two inequalities in Theorem 3.4.20 in the classic “Analytic Inequalities” by Mitrinovic are corrected, and the corresponding inequalities for circular functions and hyperbolic ...

Authors: Ling Zhu

Pointwise approximation of modified conjugate functions by matrix operators of conjugate Fourier series of \(2\pi /r\)-periodic functions

We extend the results of Xh. Z. Krasniqi (Acta Comment. Univ. Tartu Math. 17:89–101, 2013) and the authors (Acta Comment. Univ. Tartu Math. 13:11–24, 2009; Proc. Est. Acad. Sci. 67:50–60, 2018) to the case when c...

Authors: Mateusz Kubiak, Włodzimierz Łenski and Bogdan Szal

Existence and uniqueness result for a class of mixed variational problems

Our aim in this paper is to investigate the existence and uniqueness result for a class of mixed variational problems. They are governed by two variational inequalities. By applying the saddle-point theory, we...

Authors: Caijing Jiang

Variation and oscillation for the multilinear singular integrals satisfying Hörmander type conditions

Authors: Yinhong Xia