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  1. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:141

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  2. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:140

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  3. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:137

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  4. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:134

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  5. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:131

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  6. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:130

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  7. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:129

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  8. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:128

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  9. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:127

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  10. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:125

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  11. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:120

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  12. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:117

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  13. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:115

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  14. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:114

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  15. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:113

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  16. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:111

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  17. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:110

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  18. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:104

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  19. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:103

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  20. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:101

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  21. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:99

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  22. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:98

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  23. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:97

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  24. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:96

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  25. Content type: Retraction Note

    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

    Citation: Journal of Inequalities and Applications 2019 2019:95

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    The original article was published in Journal of Inequalities and Applications 2018 2018:298

  26. Content type: Research

    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

    Citation: Journal of Inequalities and Applications 2019 2019:93

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