Journal Of Inequalities Research Articles

Preface

On behalf of the International Advisory Board and the Local Organizing Committee of The International Congress in Honour of Professor Hari M. Srivastava, which was held in the Auditorium at the Campus of Uludag University, Bursa, Turkey on August 23-26, 2012, and on our own behalves, we would like to express our happiness and gratitude to all participants who attended and actively participated in our Congress. 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’.

Preface

On behalf of the International Advisory Board and the Local Organizing Committee of The International Congress in Honour of Professor Hari M. Srivastava, which was held in the Auditorium at the Campus of Uludag University, Bursa, Turkey on August 23-26, 2012, and on our own behalves, we would like to express our happiness and gratitude to all participants who attended and actively participated in our Congress.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’.

Preface

On behalf of the International Advisory Board and the Local Organizing Committee of The International Congress in Honour of Professor Hari M. Srivastava, which was held in the Auditorium at the Campus of Uludag University, Bursa, Turkey on August 23-26, 2012, and on our own behalves, we would like to express our happiness and gratitude to all participants who attended and actively participated in our Congress. 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’.

Preface

On behalf of the International Advisory Board and the Local Organizing Committee of The International Congress in Honour of Professor Hari M. Srivastava, which was held in the Auditorium at the Campus of Uludag University, Bursa, Turkey on August 23-26, 2012, and on our own behalves, we would like to express our happiness and gratitude to all participants who attended and actively participated in our Congress.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’.

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’.

A note on ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210’

Abstract In this note, we emphasize that the proofs and statements of the main results of the paper ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces’ (Journal of Inequalities and Applications 2013, 2013:210) do not have any utility to use the partial metric. Hence, it has no contribution to either partial metric theory or Caristi-type fixed point problems. MSC:47H10, 54H25.

A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques

Abstract In this note, we use a procedure, proposed in [Bianchi, M., and A. Torriero, Some localization theorems using a majorization technique, Journal of Inequalities and Applications 5 (2000), 433–446], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [Bianchi M., A. Cornaro, J.L. Palacios and A. Torriero, Bounds for the Kirkhhoff index via majorization techniques, Journal of Mathematical Chemistry, (2012) online first]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.

Erratum for: The Hermite-Hadamard inequality for r-convex functions [Journal of Inequalities and Applications 2012, 2012:215

Erratum for: The Hermite-Hadamard inequality for r-convex functions [Journal of Inequalities and Applications 2012, 2012:215

Optimal Two Parameter Bounds for the Seiffert Mean

We obtain sharp bounds for the Seiffert mean in terms of a two parameter family of means. Our results generalize and extend the recent bounds presented in the Journal of Inequalities and Applications (2012) and Abstract and Applied Analysis (2012).

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’.

A trigonometric double-inequality

Trigonometric functions, in particular the sine and cosine functions, play a relevant role in physics and various branches of mathematics. In view of their importance the properties of these functions have been studied intensively. Of special interest are inequalities for trigonometric functions. In his classical book Analytic Inequalities D.S. Mitrinovic dedicated a whole section to this subject. In the recent past, several authors discovered remarkable new inequalities for sine, cosine, and their relatives. Many of them appeared in the Journal of Inequalities in Pure and Applied Mathematics, in Mathematical Inequalities and Applications, and in the Journal of Inequalities and Applications.

Further Results for Perron–Frobenius Theorem for Nonnegative Tensors

For a nonnegative irreducible tensor, we give distribution properties of its eigenvalues. In particular, the spectral radius of a nonnegative irreducible tensor with positive trace is proved to be the unique eigenvalue on the spectral circle. Unlike the matrix setting, we give an example to present that this type of tensor is not always primitive. Thus, for a nonnegative irreducible tensor, the primitivity is a sufficient condition only for the spectral radius to be the unique eigenvalue on the spectral circle. Also, the stochastic tensor is defined, and we show that every nonnegative irreducible tensor with unit spectral radius is diagonally similar to a certain irreducible stochastic tensor. Based on this result, the minimax theorem for tensors is proved by using an alternative approach. Further, with the help of the minimax theorem, we illustrate that the problem of finding the spectral radius (largest singular value) of a nonnegative irreducible square (rectangular) tensor can be converted into a convex optimization problem. Additionally, we give an equivalent condition of irreducible nonnegative tensors. By this condition, one can easily determine whether or not a nonnegative tensor is irreducible.

Strong Convergence Theorems by an Extragradient Method for Solving Variational Inequalities and Equilibrium Problems in a Hilbert Space

In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for monotone, Lipschitz-continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges strongly to a common element of the above three sets under some parametric controlling conditions. This main theorem extends a recent result of Yao, Liou and Yao [Y. Yao, Y. C. Liou and J.-C. Yao, ''An Extragradient Method for Fixed Point Problems and Variational Inequality Problems,'' Journal of Inequalities and Applications Volume 2007, Article ID 38752, 12 pages doi:10.1155/2007/38752] and many others.

Euler harmonic identities and moments of real Borel measures

[1] A. CIVLJAK, LJ. DEDIC AND M. MATIC, On Ostrowski and Euler-Gruss type inequalities involving measures, Journal of Mathematical Inequalities, 1, 1 (2007), 65–81. [2] A. CIVLJAK, LJ. DEDIC AND M. MATIC, On an integration-by-parts formula for measures, Journal of Inequalities in Pure and Applied Mathematics, 8, 4 (2007), Article 93, 13 pp. [3] A. CIVLJAK, LJ. DEDIC AND M. MATIC, Euler-Gruss type inequalities involving measures, International Series of Numerical Mathematics, Birkhauser Verlag Basel/Switzerland, Vol. 157 (2008), 109– 120, 2008. [4] A. CIVLJAK, LJ. DEDIC AND M. MATIC,Euler harmonic identities for measures, Nonlinear Functional Analysis and Applications, 12, 3 (2007), 343–361. [5] M. MATIC, J. PECARIC AND N. UJEVIC,Generalizations of weighted version of Ostrowski’s inequality and some related results, Journal of Inequalities and Applications, 5 (2000), 639–666.

On Ostrowski and Euler-Grüss type inequalities involving measures

[1] A. CIVLJAK, LJ. DEDIC AND M. MATIC, On an integration-by-parts formula for measures, To appear (submitted to International Journal of Pure and Applied Mathematics). [2] A. CIVLJAK, LJ. DEDIC AND M. MATIC, Euler-Gruss type inequalities involving measures, To appear (submitted to Elsevier, JMAA, Nov 19, 2006). [3] M. MATIC, J. PECARIC AND N. UJEVIC, Generalizations of weighted version of Ostrowski’s inequality and some related results, Journal of Inequalities and Applications, 2000, Vol. 5, pp. 639–666.

The dilogarithm function for complex argument

This paper summarizes the basic properties of the Euler dilogarithm function, often referred to as the Spence function. These include integral representations, series expansions, linear and quadrat...

On the non-universality of the error function in the smoothing of stokes discontinuities

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Chapman S. J. 1996On the non-universality of the error function in the smoothing of stokes discontinuitiesProc. R. Soc. Lond. A.4522225–2230http://doi.org/10.1098/rspa.1996.0118SectionRestricted accessArticleOn the non-universality of the error function in the smoothing of stokes discontinuities S. J. Chapman Google Scholar Find this author on PubMed Search for more papers by this author S. J. Chapman Google Scholar Find this author on PubMed Search for more papers by this author Published:01 January 1996https://doi.org/10.1098/rspa.1996.0118AbstractThe non-universality of the error function in the smoothing of Stokes lines is demonstrated by means of an example with smoothing function ∫ ϕ-∞ e -u2m+g(u) du, where m is any integer greater than 2 and g is any polynomical of degree less than or equal to 2m - 1.FootnotesThis text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Say F (2020) Optimal successive complementary expansion for singular differential equations, Mathematical Methods in the Applied Sciences, 10.1002/mma.6228, 44:9, (7423-7432), Online publication date: 1-Jun-2021. Lustri C, Pethiyagoda R and Chapman S (2019) Three-dimensional capillary waves due to a submerged source with small surface tension, Journal of Fluid Mechanics, 10.1017/jfm.2018.1030, 863, (670-701), Online publication date: 25-Mar-2019. Dean A, Matthews P, Cox S and King J (2015) Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice, SIAM Journal on Applied Dynamical Systems, 10.1137/140966897, 14:1, (481-521), Online publication date: 1-Jan-2015. Chu Y, Li Y, Xia W and Zhang X (2014) Best possible inequalities for the harmonic mean of error function, Journal of Inequalities and Applications, 10.1186/1029-242X-2014-525, 2014:1, (525), . Pasquetti S and Schiappa R (2010) Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models, Annales Henri Poincaré, 10.1007/s00023-010-0044-5, 11:3, (351-431), Online publication date: 1-Aug-2010. Chapman S, King J and Adams K (1998) Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454:1978, (2733-2755), Online publication date: 8-Oct-1998. Xia W (2012) Two Optimal Double Inequalities for Error Function, Advanced Materials Research, 10.4028/www.scientific.net/AMR.557-559.2092, 557-559, (2092-2095) This Issue08 October 1996Volume 452Issue 1953 Article InformationDOI:https://doi.org/10.1098/rspa.1996.0118Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Manuscript received24/08/1995Manuscript accepted11/12/1995Published online01/01/1997Published in print01/01/1996 License:Scanned images copyright © 2017, Royal Society Citations and impact

The Solution of Systems of Piecewise Linear Equations

The Solution of Systems of Piecewise Linear Equations

Inequalities for Special Functions (D. K. Ross)

Previous article Next article Inequalities for Special Functions (D. K. Ross)D. J. BordelonD. J. Bordelonhttps://doi.org/10.1137/1015083PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yudell L. Luke, The special functions and their approximations, Vol. I, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York, 1969xx+349 MR0241700 0193.01701 Google Scholar[2] A. L. Jones, An extension of an inequality involving modified Bessel functions, J. Math. and Phys., 47 (1968), 220–221 MR0227483 0159.09603 CrossrefISIGoogle Scholar[3] D. K. Rosenthal, The shape and stability of a bubble at the axis of a rotating liquid, J. Fluid Mech., 12 (1962), 358–366 0107.19704 CrossrefISIGoogle Scholar[4] D. K. Ross, The stability of a column of liquid to torsional oscillations, Z. Angew. Math. Phys., 21 (1970), 137–140 10.1007/BF01594991 0185.55201 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Uniform Structural Stability of Hagen–Poiseuille Flows in a Pipe3 May 2022 | Communications in Mathematical Physics, Vol. 393, No. 3 Cross Ref Monotonicity and inequalities involving the modified Bessel functions of the second kindJournal of Mathematical Analysis and Applications, Vol. 508, No. 2 Cross Ref Bounds for modified Struve functions of the first kind and their ratiosJournal of Mathematical Analysis and Applications, Vol. 468, No. 1 Cross Ref Two-sided inequalities for the Struve and Lommel functions9 February 2018 | Quaestiones Mathematicae, Vol. 41, No. 7 Cross Ref On approximating the modified Bessel function of the second kind13 February 2017 | Journal of Inequalities and Applications, Vol. 2017, No. 1 Cross Ref ML Detection in Phase Noise Impaired SIMO Channels With Uplink TrainingIEEE Transactions on Communications, Vol. 64, No. 1 Cross Ref Bounds for modified Bessel functions of the first and second kinds5 August 2010 | Proceedings of the Edinburgh Mathematical Society, Vol. 53, No. 3 Cross Ref Log-convexity and log-concavity of hypergeometric-like functionsJournal of Mathematical Analysis and Applications, Vol. 364, No. 2 Cross Ref Inequalities involving Bessel and modified Bessel functionsJournal of Mathematical Analysis and Applications, Vol. 147, No. 1 Cross Ref An Inequality for the Bessel Function $J_\nu (\nu x)$R. B. Paris17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 15, No. 1AbstractPDF (177 KB)Inequalities for Ratios of Integrals Cross Ref Rational Bounds for Ratios of Modified Bessel FunctionsIngemar Nåsell17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 9, No. 1AbstractPDF (782 KB)Inequalities for hypergeometric functionsMathematics of Computation, Vol. 30, No. 134 Cross Ref Volume 15, Issue 3| 1973SIAM Review History Published online:18 July 2006 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1015083Article page range:pp. 665-670ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics