The Experts below are selected from a list of 32169 Experts worldwide ranked by ideXlab platform
Árpád Baricz - One of the best experts on this subject based on the ideXlab platform.
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Turán type inequalities for confluent hypergeometric functions of the second kind
Studia Scientiarum Mathematicarum Hungarica, 2016Co-Authors: Árpád Baricz, Saminathan Ponnusamy, Sanjeev SinghAbstract:In this paper we deduce some tight Turan type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some already established Turan type inequalities. Moreover, by using these Turan type inequalities, we deduce some new inequalities for Tricomi confluent hypergeometric functions of the second kind. The key tool in the proof of the Turan type inequalities is an integral representation for a quotient of Tricomi confluent hypergeometric functions, which arises in the study of the infinite divisibility of the Fisher-Snedecor F distribution.
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Turan type inequalities for some lommel functions of the first kind
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Árpád Baricz, Stamatis KoumandosAbstract:In this paper certain Turan-type inequalities for some Lommel functions of the first kind are deduced. The key tools in our proofs are the infinite product representation for these Lommel functions of the first kind, a classical result of Polya on the zeros of some particular entire functions, and the connection of these Lommel functions with the so-called Laguerre–Polya class of entire functions. Moreover, it is shown that in some cases Steinig's results on the sign of Lommel functions of the first kind combined with the so-called monotone form of l’Hospital's rule can be used in the proof of the corresponding Turan-type inequalities.
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Turán type inequalities for generalized inverse trigonometric functions
Filomat, 2015Co-Authors: Árpád Baricz, Barkat Ali Bhayo, Matti VuorinenAbstract:In this paper we study the inverse of the eigenfunction sinp of the one-dimensional p-Laplace operator and its dependence on the parameter p, and we present a Turan type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Turan type inequality for a series considered by Ramanujan, involving the digamma function
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Turán determinants of Bessel functions
Forum Mathematicum, 2014Co-Authors: Árpád Baricz, Tibor K. PogányAbstract:In this paper our aim is to survey the Turan type inequalities and related problems for the Bessel functions of the first kind. Moreover, we extend the known higher order Turan type inequalities for Bessel functions of the first kind to real parameters and we deduce new closed integral representation formulae for the second kind Neumann type series of Bessel functions of the first kind occurring in the study of Turan determinants of Bessel functions of the first kind. At the end of the paper we prove a Turan type inequality for the Bessel functions of the second kind.
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Turan type inequalities for tricomi confluent hypergeometric functions
Constructive Approximation, 2013Co-Authors: Árpád Baricz, Mourad E. H. IsmailAbstract:Some sharp two-sided Turan type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher–Snedecor F distribution. Moreover, some complete monotonicity results are given concerning Turan determinants of Tricomi confluent hypergeometric functions. These complement and improve some of the results of Ismail and Laforgia (in Constr. Approx. 26:1–9, 2007).
Kendall C Richards - One of the best experts on this subject based on the ideXlab platform.
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a note on Turan type and mean inequalities for the kummer function
Journal of Mathematical Analysis and Applications, 2009Co-Authors: Roger W Barnard, Michael B Gordy, Kendall C RichardsAbstract:Abstract Turan-type inequalities for combinations of Kummer functions involving Φ ( a ± ν , c ± ν , x ) and Φ ( a , c ± ν , x ) have been recently investigated in [A. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. 26 (3) (2008) 279–293; M.E.H. Ismail, A. Laforgia, Monotonicity properties of determinants of special functions, Constr. Approx. 26 (2007) 1–9]. In the current paper, we resolve the corresponding Turan-type and closely related mean inequalities for the additional case involving Φ ( a ± ν , c , x ) . The application to modeling credit risk is also summarized.
Vera T. Sós - One of the best experts on this subject based on the ideXlab platform.
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Ramsey—Turán theory
Discrete Mathematics, 2001Co-Authors: Miklós Simonovits, Vera T. SósAbstract:Abstract Ramsey- and Turan-type problems were always strongly related to each other. Motivated by an observation of Paul Erdős, it was Turan who started the systematic investigation of the applications of extremal graph theory in geometry and analysis. This led the second author to some results and problems which, in turn, led to the birth of Ramsey–Turan-type theorems. Today this is a wide field of research with many interesting results and many unsolved problems. Below we give a short survey of the most important parts of this field: starting with a historical sketch we continue by describing the 1. Ramsey–Turan-type problems and results. 2. Related problems in Ramsey theory. 3. Some applications.
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ramsey Turan theory
Discrete Mathematics, 2001Co-Authors: Miklós Simonovits, Vera T. SósAbstract:Abstract Ramsey- and Turan-type problems were always strongly related to each other. Motivated by an observation of Paul Erdős, it was Turan who started the systematic investigation of the applications of extremal graph theory in geometry and analysis. This led the second author to some results and problems which, in turn, led to the birth of Ramsey–Turan-type theorems. Today this is a wide field of research with many interesting results and many unsolved problems. Below we give a short survey of the most important parts of this field: starting with a historical sketch we continue by describing the 1. Ramsey–Turan-type problems and results. 2. Related problems in Ramsey theory. 3. Some applications.
Roger W Barnard - One of the best experts on this subject based on the ideXlab platform.
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a note on Turan type and mean inequalities for the kummer function
Journal of Mathematical Analysis and Applications, 2009Co-Authors: Roger W Barnard, Michael B Gordy, Kendall C RichardsAbstract:Abstract Turan-type inequalities for combinations of Kummer functions involving Φ ( a ± ν , c ± ν , x ) and Φ ( a , c ± ν , x ) have been recently investigated in [A. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. 26 (3) (2008) 279–293; M.E.H. Ismail, A. Laforgia, Monotonicity properties of determinants of special functions, Constr. Approx. 26 (2007) 1–9]. In the current paper, we resolve the corresponding Turan-type and closely related mean inequalities for the additional case involving Φ ( a ± ν , c , x ) . The application to modeling credit risk is also summarized.
József Balogh - One of the best experts on this subject based on the ideXlab platform.
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On two problems in ramsey-turán theory
SIAM Journal on Discrete Mathematics, 2017Co-Authors: József Balogh, Hong Liu, Maryam SharifzadehAbstract:Alon, Balogh, Keevash, and Sudakov proved that the $(k-1)$-partite Turan graph maximizes the number of distinct $r$-edge-colorings with no monochromatic $K_k$ for all fixed $k$ and $r=2,3$, among all $n$-vertex graphs. In this paper, we determine this function asymptotically for $r=2$ among $n$-vertex graphs with a sublinear independence number. Somewhat surprisingly, unlike Alon, Balog, Keevash, and Sudakov's result, the extremal construction from Ramsey--Turan theory, as a natural candidate, does not maximize the number of distinct edge-colorings with no monochromatic cliques among all graphs with a sublinear independence number, even in the 2-colored case. In the second problem, we determine the maximum number of triangles asymptotically in an $n$-vertex $K_k$-free graph $G$ with $\alpha(G)=o(n)$. The extremal graphs have a similar structure to the extremal graphs for the classical Ramsey--Turan problem, i.e., when the number of edges is maximized.
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The Turán density of triple systems is not principal
Journal of Combinatorial Theory Series A, 2002Co-Authors: József BaloghAbstract:The Erdos-Stone-Simonovits Theorem implies that the Turan density of a family of graphs is the minimum of the Turan densities of the individual graphs from the family. It was conjectured by Mubayi and Rodl (J. Combin. Theory Ser. A, submitted) that this is not necessarily true for hypergraphs, in particular for triple systems. We give an example, which shows that their conjecture is true.
