Journal Of Inequalities Research Articles

Normalized fractional inequalities for continuous random variables

We introduce new normalized fractional integral concepts on random variables. We also introduce the fractional coupled random variables. The Jensen integral inequality is generalized. Also, some fractional bounds estimating the expectation and variance are delivered. At the end, some other results related to the coupled random variables are proved. For this work, some results of the papers [On some statistical and probability inequalities. Journal of Inequalities and Special Functions, 2016] and [Some inequalities for the expectation and variance of a random variable whose PDFs are absolutely continuous using a pre-Chebychev inequality. Tamkang Journal of Mathematics, 2001] are deduced as some special cases.

A NEW APPROACH TO THE STUDY OF FIXED POINT THEORY FOR EXPANSIVE MAPPINGS

Fixed Point Theory has become one of the most beneficial branches of Nonlinear Analysis due to its possible applications. In 2017, Ahmad et al. [Journal of Nonlinear Sciences and Applications, 10 (2017), 2350-2358] extended and modified the notion of θ-contraction introduced by Jleli and Samet [Journal of Inequalities and Applications, 38 (2014)] to metric spaces. Also, Khojasteh et al. [Filomat,29 (2015), 1189-1194] introduced the notion of simulation function in order to express different contractivity conditions in a unified way and proved some related fixed point results. To complement these notions, in this paper, we introduce two new types of expansive mappings called θ-expansion and Z-expansion. The related fixed point theorems are also proved. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.

Inequalities for generalized eigenvalues of quaternion matrices

Studying eigenvalues of square matrices is a traditional and fundamental direction in linear algebra. Quaternion matrices constitute an important and extensively useful subclass of square matrices. In the paper, the authors (1) introduce the concept of “generalized eigenvalues of quaternion matrix”; (2) give some properties of generalized eigenvalues for a regular quaternion matrix pair; (3) establish inequalities, the min–max theorem, and the perturbation theorem for generalized eigenvalues of a regular quaternion matrix pair; (4) and weaken conditions of Theorem 2.1 in a paper published in 2018 at the Journal of Inequalities and Applications.

New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application

In this paper, inspired by Jleli and Samet (Journal of Inequalities and Applications 38 (2014) 1–8), we introduce two new classes of auxiliary functions and utilize the same to define ( θ , ψ ) R -weak contractions. Utilizing ( θ , ψ ) R -weak contractions, we prove some fixed point theorems in the setting of relational metric spaces. We employ some examples to substantiate the utility of our newly proven results. Finally, we apply one of our newly proven results to ensure the existence and uniqueness of the solution of a Volterra-type integral equation.

Least-Square-Based Three-Term Conjugate Gradient Projection Method for ℓ1-Norm Problems with Application to Compressed Sensing

In this paper, we propose, analyze, and test an alternative method for solving the ℓ 1 -norm regularization problem for recovering sparse signals and blurred images in compressive sensing. The method is motivated by the recent proposed nonlinear conjugate gradient method of Tang, Li and Cui [Journal of Inequalities and Applications, 2020(1), 27] designed based on the least-squares technique. The proposed method aims to minimize a non-smooth minimization problem consisting of a least-squares data fitting term and an ℓ 1 -norm regularization term. The search directions generated by the proposed method are descent directions. In addition, under the monotonicity and Lipschitz continuity assumption, we establish the global convergence of the method. Preliminary numerical results are reported to show the efficiency of the proposed method in practical computation.

A New Generalized Inequality for Covariance in N Dimensions

Inspired by the work of Zhefei He and Mingjin Wang which was published in the Journal of Inequalities and Applications in 2015, this paper further generalizes some related results to the case of multidimensional random variables. The resulting inequality for covariance is then applied to different multidimensional statistical distributions (multiuniform, multinomial, and multinormal). Coordinate dependence of the inequality is also examined. The obtained formulas could be useful for making estimates in multivariate statistics.

Value distribution for nth difference operator of meromorphic functions with maximal deficiency sum

In this paper, we obtain the relationship between the characteristic function of meromorphic function having maximal deficiency sum and its higher order exact difference. We improve and generalise several results of Zhaojun Wu (Journal of Inequalities and Applications 530, [3]) to a great extent. We obtain an analogue of Shah and Singh (Mathematische Zeitschrift 65:171–174, [4]) in an improved form for $$\Delta _{c}f$$ . Also we establish a lower bound for $$K(\Delta _{c}f)=\limsup \limits _{r\rightarrow \infty }\frac{N\left( r,\Delta _{c}f\right) +N\left( r,\frac{1}{\Delta _{c}f}\right) }{T(r,\Delta _{c}f)}$$ . Under certain conditions we also show that $$K(\Delta _{c}^{n}f)=0$$ , for any integer $$n\ge 1$$ .

A descent Dai-Liao conjugate gradient method for nonlinear equations

In this work, we propose an algorithm for solving system of nonlinear equations. The idea is a combination of the descent Dai-Liao method by Babaie-Kafaki and Gambari (Optim. Meth. Soft. 29(3), 583–591, 2014) and the hyperplane projection method. Using the monotonicity and Lipschitz continuity assumptions, we prove that the proposed method is globally convergent. Examples of numerical experiment show that the method is promising and efficient compared to the method proposed by Sun et al. (Journal of Inequalities and Applications 236, 1–8, 2017).

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

Some fixed point results for dual contractions of rational type

Isik and Turkoglu [Some Fixed Point Theorems in Ordered Partial Metric Spaces, Journal of Inequalities and Special Functions, Volume 4 Issue 2(2013), Pages 13-18] established new fixed point results in complete partial metric spaces. The purpose of this paper is to introduce a dual contraction of rational type and to obtain some new fixed point results in dual partial metric spaces for dominating and dominated mappings. These results extend various comparable results existing in literature. Moreover, we give an example that shows the usefulness and effectiveness of these results among corresponding fixed point theorems established in partial metric spaces.

Results on n-tupled fixed points in complete ordered metric spaces.

The aim of this paper is to study n-tupled coincidence and n-tupled fixed point results, a new notion propounded by M.Imdad et.al.[13] for compatible maps in partially ordered metric spaces. Our results generalize, extend and improve the coupled fixed point results of Bhaskar and Lakshmikantham, Nonlinear Analysis: Theory, Methods and Applications, vol.65, no.7, 2006, pp. 1379-1393, V. Lakshmikantham and L. Ciric, Nonlinear Analysis, Theory, Method and Applications, vol. 70, no12, 2009, pp. 4341-4349, tripled fixed point theorems by Berinde and Borcut, Nonlinear Analysis, Volume 74, Issue 15, October 2011, Pages 4889-4897, Quadruple fixed point theorems by E. Karapinar and V. Berinde, Banach Journal of Mathematical Analysis , vol. 6, no. 1, pp. 74–89, 2012 and multidimensional fixed point results by Muzeyyen Erturk and Vatan Karakaya, Journal of Inequalities and Applications 2013, 2013:196, pp. 1-19, M. Imdad, A. H. Soliman, B. S. Choudhary and P. Das, Journal of Operators, Volume 2013, Article ID 532867, pp. 1-8 and M. Paknazar, M. E. Gordji, M. D. L. Sen and S. M. Vaezpour, Fixed Point Theory and Applications 2013, 2013 :11 etc.

Fixed Point Theorems for Generalized \((\alpha,\psi)\)-Expansive Mappings in Generalized Metric Spaces

The aim of this paper is to introduce new notion of generalized \((\alpha,\psi)\)-expansive mappings in generalized metric spaces and to study the existence of a fixed point for the mappings in this space. Our new notion complements the concept of generalized \((\alpha,\psi)\)-contractions on generalized metric spaces introduced recently by Aydi et al. (Journal of Inequalities and Applications 2014, 229 (2014)). The presented theorems extend, generalize and improve many existing results in the literature.

On Ray's theorem for weak firmly nonexpansive mappings in Hilbert Spaces

In this work, we introduce notions of generalized firmly nonexpansive (G-firmly non expansive) and fundamentally firmly nonexpansive (F-firmly nonexpansive) mappings and utilize to the same to prove Ray's theorem for G-firmly and F-firmly nonexpansive mappings in Hilbert Spaces. Our results extend the result due to F. Kohsaka [ Ray's theorem revisited: a fixed point free firmly nonexpansive mapping in Hilbert spaces, Journal of Inequalities and Applications (2015) 2015:86 ].

Some New Impulsive Integral Inequalities

Some new impulsive integral inequalities related to certain integral inequalities are established, which extend the results proved by J. Li in [On some new impulsive integral inequalities, Journal of Inequalities and Applications, Vol. 200. The inequalities given here can be used as basic tools in the qualitative theory of certain impulsive differential and integral equations.

Some Remarks on Multidimensional Fixed Point Theorems in Partially Ordered Metric Spaces.

In this paper , we show that multidimensional ( coupled, tripled, quadrupled, n-tupled) theorems can be reduced to unidimensional fixed point theorems. . Our results generalize, extend and improve the coupled fixed point results of Bhaskar and Lakshmikantham, Nonlinear Analysis: Theory, Methods and Applications, vol.65, no.7, 2006, pp. 1379-1393, V. Lakshmikantham and L. Ciric, Nonlinear Analysis, Theory, Method and Applications, vol. 70, no12, 2009, pp. 4341-4349, tripled fixed point theorems by Berinde and Borcut, Nonlinear Analysis, Volume 74, Issue 15, October 2011, Pages 4889-4897, Quadruple fixed point theorems by E. Karapinar and V. Berinde, Banach Journal of Mathematical Analysis, vol. 6, no. 1, pp. 74–89, 2012 and multidimensional fixed point results by Muzeyyen Erturk and Vatan Karakaya, Journal of Inequalities and Applications 2013, 2013:196, pp. 1-19, M. Imdad, A. H. Soliman, B. S. Choudhary and P. Das, Journal of Operators, Volume 2013, Article ID 532867, pp. 1-8 and M. Paknazar, M. E. Gordji, M. D. L. Sen and S. M. Vaezpour, Fixed Point Theory and Applications 2013, 2013:11 etc.

Meromorphic functions sharing fixed points and poles with finite weights

Abstract In the paper, with the aid of weighted sharing method we study the problems of meromorphic functions that share fixed points (or a nonzero finite value) and poles with finite weights. The results of the paper improve some recent results due to Y. H. Cao and X. B. Zhang [Journal of Inequalities and Applications, 2012:100].

Foreword

Foreword for the Proceedings of the International Congress in Honour of Professor Hari M. Srivastava. This article is being published in each of the four Special Issues of the SpringerOpen journals, Advances in Difference Equations, Boundary Value Problems, Fixed Point Theory and Applications and Journal of Inequalities and Applications, which are entitled ‘Proceedings of the International Congress in Honour of Professor Hari M. Srivastava’.

A note on ‘n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces’

In this note, we show that multidimensional fixed point theorems established in the recent report [M. Ertürk and V. Karakaya, n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces, Journal of Inequalities and Applications 2013, 2013:196] have gaps. Furthermore, the results of the mentioned paper can be reduced to unidimensional (existing) fixed point theorems.MSC:47H10, 54H25.

Professor H. M. Srivastava: man and mathematician

Biography of Professor Hari M. Srivastava.This article is being published in each of the four Special Issues of the SpringerOpen journals, Advances in Difference Equations, Boundary Value Problems, Fixed Point Theory and Applications and Journal of Inequalities and Applications, which are entitled ‘Proceedings of the International Congress in Honour of Professor Hari M. Srivastava’.

Professor H. M. Srivastava: man and mathematician

Biography of Professor Hari M. Srivastava. This article is being published in each of the four Special Issues of the SpringerOpen journals, Advances in Difference Equations, Boundary Value Problems, Fixed Point Theory and Applications and Journal of Inequalities and Applications, which are entitled ‘Proceedings of the International Congress in Honour of Professor Hari M. Srivastava’.