Articles

Riemann–Liouville fractional stochastic evolution equations driven by both Wiener process and fractional Brownian motion

This article is devoted to the study of the existence and uniqueness of mild solution to a class of Riemann–Liouville fractional stochastic evolution equations driven by both Wiener process and fractional Brow...

Authors: Min Yang and Haibo Gu

Refinements of some integral inequalities for unified integral operators

In this paper we are presenting the refinements of integral inequalities established for convex functions. Consequently, we get refinements of several fractional integral inequalities for different kinds of fr...

Authors: Chahn Yong Jung, Ghulam Farid, Maja Andrić, Josip Pečarić and Yu-Ming Chu

Dunkl-type generalization of the second kind beta operators via \((p,q)\)-calculus

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

Convergence rate of Euler–Maruyama scheme for SDDEs of neutral type

In this paper, we are concerned with the convergence rate of Euler–Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral, drift, and diffusion terms are allow...

Authors: Yanting Ji

Error estimates of finite volume method for Stokes optimal control problem

In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal

Authors: Lin Lan, Ri-hui Chen, Xiao-dong Wang, Chen-xia Ma and Hao-nan Fu

Some new dynamic inequalities with several functions of Hardy type on time scales

The aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited ca...

Authors: Adnane Hamiaz, Waleed Abuelela, Samir H. Saker and Dumitru Baleanu

Sharp blowup rate for NLS with a repulsive harmonic potential

Authors: Rui Zhou

On Cesàro and Copson sequence spaces with weights

In this paper, we prove some properties of weighted Cesàro and Copson sequences spaces by establishing some factorization theorems. The results lead to two-sided norm discrete inequalities with best possible c...

Authors: S. H. Saker, Maryam M. Abuelwafa, Ahmed M. Zidan and Dumitru Baleanu

New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

A specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized inco...

Authors: Pshtiwan Othman Mohammed, Thabet Abdeljawad, Dumitru Baleanu, Artion Kashuri, Faraidun Hamasalh and Praveen Agarwal

Recovering differential pencils with spectral boundary conditions and spectral jump conditions

In this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems:

Authors: Yasser Khalili and Dumitru Baleanu

Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseud...

Authors: Lateef Olakunle Jolaoso and Maggie Aphane

Refinements of some Hardy–Littlewood–Pólya type inequalities via Green’s functions and Fink’s identity and related results

In this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex functions. We also present refi...

Authors: Sadia Khalid and Josip Pečarić

A reverse Hardy–Hilbert-type integral inequality involving one derivative function

In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral...

Authors: Qian Chen and Bicheng Yang

The Picard-HSS-SOR iteration method for absolute value equations

In this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergenc...

Authors: Lin Zheng

Periodic solutions with prescribed minimal period to Hamiltonian systems

In this article, we study the existence of periodic solutions to second order Hamiltonian systems. Our goal is twofold. When the nonlinear term satisfies a strictly monotone condition, we show that, for any

Authors: Huafeng Xiao and Zupei Shen

On the qualitative behavior of the solutions to second-order neutral delay differential equations

Differential equations of second order appear in numerous applications such as fluid dynamics, electromagnetism, quantum mechanics, neural networks and the field of time symmetric electrodynamics. The aim of t...

Authors: Shyam Sundar Santra, Hammad Alotaibi and Omar Bazighifan

New inertial proximal gradient methods for unconstrained convex optimization problems

The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity app...

Authors: Peichao Duan, Yiqun Zhang and Qinxiong Bu

Hardy operators and the commutators on Hardy spaces

In this paper, the boundedness of the classic Hardy operator and its adjoint on Hardy spaces is obtained. We also discuss the boundedness for the commutators generated by the classic Hardy operator and its adj...

Authors: Zhuang Niu, Shasha Guo and Wenming Li

The connectedness of the solutions set for set-valued vector equilibrium problems under improvement sets

In this paper, we provide the connectedness of the sets of weak efficient solutions, Henig efficient solutions and Benson proper efficient solutions for set-valued vector equilibrium problems under improvement...

Authors: Hongwei Liang, Zhongping Wan and Litao Zhang

The functional inequality for the mixed quermassintegral

Authors: Fangwei Chen, Jianbo Fang, Miao Luo and Congli Yang

Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models

We study the nonasymptotic properties of a general norm penalized estimator, which include Lasso, weighted Lasso, and group Lasso as special cases, for sparse high-dimensional misspecified Cox models with time...

Authors: Yijun Xiao, Ting Yan, Huiming Zhang and Yuanyuan Zhang

Hyers–Ulam stability of functional inequalities: a fixed point approach

Using the fixed point method, we prove the Hyers–Ulam stability of a cubic and quartic functional equation and of an additive and quartic functional equation in matrix Banach algebras.

Authors: Afshan Batool, Sundas Nawaz, Ozgur Ege and Manuel de la Sen

Multivalued weak cyclic δ-contraction mappings

In this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such...

Authors: Pulak Konar, Samir Kumar Bhandari, Sumit Chandok and Aiman Mukheimer

Generalized hypergeometric distribution and its applications on univalent functions

The purpose of the present paper is to introduce a generalized hypergeometric distribution and obtain some necessary and sufficient conditions for generalized hypergeometric distribution series belonging to ce...

Authors: Rajavadivelu Themangani, Saurabh Porwal and Nanjundan Magesh

Poly-Dedekind sums associated with poly-Bernoulli functions

Apostol considered generalized Dedekind sums by replacing the first Bernoulli function appearing in Dedekind sums by any Bernoulli functions and derived a reciprocity relation for them. Recently, poly-Dedekind...

Authors: Yuankui Ma, Dae San Kim, Hyunseok Lee and Taekyun Kim

Norm inequalities for submultiplicative functions involving contraction sector \(2 \times 2\) block matrices

Authors: Xiaoying Zhou

On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

The role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities f...

Authors: Barış Çelik, Mustafa Ç. Gürbüz, M. Emin Özdemir and Erhan Set

Identities of symmetry for Bernoulli polynomials and power sums

Identities of symmetry in two variables for Bernoulli polynomials and power sums had been investigated by considering suitable symmetric identities. T. Kim used a completely different tool, namely the p-adic Volk...

Authors: Taekyun Kim, Dae San Kim, Han Young Kim and Jongkyum Kwon

An inertial extrapolation method for multiple-set split feasibility problem

In this paper, we propose an iterative algorithm with inertial extrapolation to approximate the solution of multiple-set split feasibility problem. Based on Lopez et al. (Inverse Probl. 28(8):085004, 2012), we ha...

Authors: Guash Haile Taddele, Poom Kumam and Anteneh Getachew Gebrie

Interchanging a limit and an integral: necessary and sufficient conditions

Authors: Takashi Kamihigashi

On a variant of Čebyšev’s inequality of the Mercer type

We consider the discrete Jensen–Mercer inequality and Čebyšev’s inequality of the Mercer type. We establish bounds for Čebyšev’s functional of the Mercer type and bounds for the Jensen–Mercer functional in ter...

Authors: Anita Matković and Josip Pečarić

Applications of differential equations to characterize the base of warped product submanifolds of cosymplectic space forms

In the present, we first obtain Chen–Ricci inequality for C-totally real warped product submanifolds in cosymplectic space forms. Then, we focus on characterizing spheres and Euclidean spaces, by using the Bochne...

Authors: Akram Ali, Fatemah Mofarreh, Wan Ainun Mior Othman and Dhriti Sundar Patra

Adaptive variational discretization approximation method for parabolic optimal control problems

In this paper, we study variational discretization method for parabolic optimization problems. Firstly, we obtain some convergence and superconvergence analysis results of the approximation scheme. Secondly, w...

Authors: Yuelong Tang and Yuchun Hua

A study on Copson operator and its associated sequence space II

Authors: Hadi Roopaei

Orbital stability of solitary waves for the generalized long-short wave resonance equations with a cubic-quintic strong nonlinear term

In this paper, we investigate the orbital stability of solitary waves for the following generalized long-short wave resonance equations of Hamiltonian form:

Authors: Xiaoxiao Zheng, Huafei Di and Xiaoming Peng

A note on maximal singular integrals with rough kernels

In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebe...

Authors: Xiao Zhang and Feng Liu

Extraction new results of common fixed point theorems for \(({T}, {\alpha }_{{s}}, {F})\)-contraction of six mappings in a tripled b-metric space with an application of integral equations

Authors: Ghorban Khalilzadeh Ranjbar and Mohammad Esmael Samei

A natural Frenet frame for null curves on the lightlike cone in Minkowski space \(\mathbb{R} ^{4}_{2}\)

Authors: Nemat Abazari, Martin Bohner, Ilgin Sağer, Alireza Sedaghatdoost and Yusuf Yayli

The solvability of a kind of generalized Riemann–Hilbert problems on function spaces \(H_{\ast }\)

In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss methods of solving R-HPs with two unknown functions and obtain ...

Authors: Pingrun Li

On structure of discrete Muckenhoupt and discrete Gehring classes

Authors: S. H. Saker, S. S. Rabie, Ghada AlNemer and M. Zakarya

Global existence of classical solutions to the two-dimensional compressible Boussinesq equations in a square domain

In this paper, we consider the initial boundary value problem of two-dimensional isentropic compressible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based on the ti...

Authors: Xucheng Huang, Zhaoyang Shang and Na Zhang

Coderivatives and Aubin property of efficient point and efficient solution set-valued maps in parametric vector optimization

The aim of this paper is computing the coderivatives of efficient point and efficient solution set-valued maps in a parametric vector optimization problem. By using a method different from the existing literat...

Authors: Xiaowei Xue

Approximately two-dimensional harmonic \((p_{1},h_{1})\)-\((p_{2},h_{2})\)-convex functions and related integral inequalities

Authors: Saad Ihsan Butt, Artion Kashuri, Muhammad Nadeem, Adnan Aslam and Wei Gao

On post quantum estimates of upper bounds involving twice \((p,q)\)-differentiable preinvex function

Authors: Muhammad Uzair Awan, Sadia Talib, Muhammad Aslam Noor, Yu-Ming Chu and Khalida Inayat Noor

Modified Krasnoselski–Mann iterative method for hierarchical fixed point problem and split mixed equilibrium problem

In this paper, we introduce a modified Krasnoselski–Mann type iterative method for capturing a common solution of a split mixed equilibrium problem and a hierarchical fixed point problem of a finite collection...

Authors: Jong Kyu Kim and Prashanta Majee

Degenerate Bell polynomials associated with umbral calculus

Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials. In recent years, studying degenerate ...

Authors: Taekyun Kim, Dae San Kim, Han-Young Kim, Hyunseok Lee and Lee-Chae Jang

A note on degenerate r-Stirling numbers

The aim of this paper is to study the unsigned degenerate r-Stirling numbers of the first kind as degenerate versions of the r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the secon...

Authors: Taekyun Kim, Dae San Kim, Hyunseok Lee and Jin-Woo Park

Solvability and algorithms of generalized nonlinear variational-like inequalities in reflexive Banach spaces

This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fix...

Authors: Haiyan Gao, Lili Wang and Liangshi Zhao

Jackknifing for partially linear varying-coefficient errors-in-variables model with missing response at random

In this paper, we focus on the response mean of the partially linear varying-coefficient errors-in-variables model with missing response at random. A simulation study is conducted to compare jackknife empirica...

Authors: Yuye Zou and Chengxin Wu

Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of...

Authors: Dafang Zhao, Muhammad Aamir Ali, Artion Kashuri, Hüseyin Budak and Mehmet Zeki Sarikaya