Journal of Inequalities and Applications

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ISSN / EISSN : 1029-242X / 1029-242X
Total articles ≅ 4,760
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Thounaojam Stephen, Yumnam Rohen, , Mairembam Bina, Nawab Hussain, Doaa Rizk
Journal of Inequalities and Applications, Volume 2021, pp 1-15; doi:10.1186/s13660-021-02661-4

Abstract:
We introduce the notion of generalized parametric metric spaces along with the study of its various properties. Further, we prove some new fixed point theorems for $(\alpha ,\psi )$ ( α , ψ ) -rational-type contractive mappings in generalized parametric metric spaces. As a consequence, we deduce fixed point theorems for $(\alpha , \psi )$ ( α , ψ ) -rational-type contractive mappings in partially ordered rectangular generalized fuzzy metric spaces.
Zunfeng Li, Haipan Shi, Yuying Qiao
Journal of Inequalities and Applications, Volume 2021, pp 1-15; doi:10.1186/s13660-021-02654-3

Abstract:
In this paper, we introduce the two-sided fractional quaternion Fourier transform (FrQFT) and give some properties of it. The main results of this paper are divided into three parts. Firstly we give a definition of the FrQFT. Secondly based on properties of the two-sided QFT, we study the relationship between the two-sided QFT and the two-sided FrQFT, and give some differential properties of the two-sided FrQFT and the Parseval identity. Finally, we give an example to illustrate the application of the two-sided FrQFT and its inverse transform in solving partial differential equations.
Jing Guo, Xianjun Zhu
Journal of Inequalities and Applications, Volume 2021, pp 1-11; doi:10.1186/s13660-021-02652-5

Abstract:
The main purpose of this paper is to show Wirtinger type inequalities for the pseudo-integral. We are concerned with pseudo-integrals based on the following three canonical cases: in the first case, the real semiring with pseudo-operation is generated by a strictly monotone continuous function g; in the second case, the pseudo-operations include a pseudo-multiplication and a power arithmetic addition; in the last case, ⊕-measures are interval-valued. Examples are given to illustrate these equalities.
Jorge Bustamante, Juan Jesús Merino-García,
Journal of Inequalities and Applications, Volume 2021, pp 1-17; doi:10.1186/s13660-021-02653-4

Abstract:
In this paper we present direct results (upper estimates) for Baskakov operators acting in spaces related with Jacobi-type weights. Our results include and extend some known facts related with this problem. The approach is based in the use of a new pointwise K-functional.
Tongxin Xu,
Journal of Inequalities and Applications, Volume 2021, pp 1-21; doi:10.1186/s13660-021-02656-1

Abstract:
In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature.
, Muhammad Nawaz Naeem, Yu-Ming Chu
Journal of Inequalities and Applications, Volume 2021, pp 1-23; doi:10.1186/s13660-021-02657-0

Abstract:
In this article, we develop a novel framework to study a new class of convex functions known as n-polynomial $\mathscr{P} $ P -convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by using a generalized k-fractional Hilfer–Katugampola derivative. We employ this technique by using the Hölder and power-mean integral inequalities. We present analogs of the Ostrowski-type integrals inequalities connected with the n-polynomial $\mathscr{P}$ P -convex function. Some new exceptional cases from the main results are obtained, and some known results are recaptured. In the end, an application to special means is given as well. The article seeks to create an exciting combination of a convex function and special functions in fractional calculus. It is supposed that this investigation will provide new directions in fractional calculus.
Hadi Roopaei, Bipan Hazarika
Journal of Inequalities and Applications, Volume 2021, pp 1-14; doi:10.1186/s13660-021-02658-z

Abstract:
In this research, we combine the Cesàro and backward difference operators of different orders which results in introducing a matrix who has two different behaviors and includes several matrices. We also investigate the Köthe duals and inclusion relations of the associated sequence space of this new matrix. Moreover, we compute the norm of this matrix on some well-known sequence spaces.
Tao Xiangxing, Zhang Qiange
Journal of Inequalities and Applications, Volume 2021, pp 1-21; doi:10.1186/s13660-021-02651-6

Abstract:
Let $(\mathcal{X}, d, \mu )$ ( X , d , μ ) be a non-homogeneous metric measure space, which satisfies the geometrically doubling condition and the upper doubling condition. In this paper, the authors prove the boundedness in $L^{p} (\mu )$ L p ( μ ) of mth-order commutators $\mathcal{M}^{\rho }_{b,m}$ M b , m ρ generated by the Log-Dini-type parametric Marcinkiewicz integral operators with RBMO functions on $(\mathcal{X}, d, \mu )$ ( X , d , μ ) . In addition, the boundedness of the mth-order commutators $\mathcal{M}^{\rho }_{b,m}$ M b , m ρ on Morrey spaces $M^{q}_{p}(\mu )$ M p q ( μ ) , $1< p \leq q< \infty $ 1 < p ≤ q < ∞ , is also obtained for the parameter $0<\rho <\infty $ 0 < ρ < ∞ .
, Matloob Anwar
Journal of Inequalities and Applications, Volume 2021, pp 1-13; doi:10.1186/s13660-021-02647-2

Abstract:
In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. Also, by using Hermite–Hadamard inequalities for the respective generalized convex functions, we find new generalized Cauchy type means.
Dandan Lai, Hailin Jin
Journal of Inequalities and Applications, Volume 2021, pp 1-15; doi:10.1186/s13660-021-02649-0

Abstract:
This paper aims to consider the dual Brunn–Minkowski inequality for log-volume of star bodies, and the equivalent Minkowski inequality for mixed log-volume.
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