Generalization of Hilbert Inequality with Some Parameters
-
S. A. A. El-Marouf
Abstract
In this paper, by introducing some parameters and estimating the weight coefficients, some new inequalities are established. All results of Hilbert, Hardy and Yang are considered as special cases of the new given inequalities.
References
[1] DEHNATH, L.-YANG, B. C.: Recent development of Hilbert-Type discrete and integral inequalities with applications, Indian J. Math. Math. Sci. 2012 (2012), 29 pp.Search in Google Scholar
[2] HARDY, G. H,-LITTLEWOOD, J. E.-POLYA, G.: Inequalities. Cambridge Univ. Press, Cambridge, 1964.Search in Google Scholar
[3] LARRY, C. A.: Special Functions of Mathematics for Engineers. McGraw-Hill Internat. Editions, McGraw-Hill, New York, 1985.Search in Google Scholar
[4] MITRINOVIC, D. S.: Analytic Inequalities. Springer-Verlag, New York-Heidelberg- Berlin, 1970.Search in Google Scholar
[5] SALEM, S. R.: Some New Hilbert Type Inequalities. Kyungpook Math. J. 46 (2006), 19-29.Search in Google Scholar
[6] WEIJIAN, J.-MINGZHE, G.: An extended Hardy-Hilbert inequality and its applications, J. Inequal. Pure Appl. Math. 7 (2006), Art. 30.Search in Google Scholar
[7] YANG, B.: On new generalizations of Hilbert’s inequality, J.Math. Anal. Appl. 48 (2000), 29-40.Search in Google Scholar
[8] YANG, B.-DEHNATH, L.: On the extended Hardy-Hilbert’s inequality, J. Math. Anal. Appl. 272 (2002), 187-199.10.1016/S0022-247X(02)00151-8Search in Google Scholar
[9] YANG, B.: A new inequality similar to Hilbert’s inequality, J. Inequal. Pure Appl. Math. 3 (2002), Art. 75. Search in Google Scholar
[10] XIE, Z.: A new Hilbert-type integral inequality with some parameters and its reverse, Kyungpook Math. J. 48 (2008), 93-100. 10.5666/KMJ.2008.48.1.093Search in Google Scholar
© Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles
Articles in the same Issue
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles
