On Applications Of The Integral Of Products OfFunctions And Its Bounds

The Steffensen inequality and bounds for the Cebysev functional are utilised to obtain bounds for some classical special functions. The technique relies on determining bounds on integrals of products of functions. The above techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function and the Zeta function.

[1]  J. F. Steffensen.  On certain inequalities between mean values, and their application to actuarial problems , 1918 .

[2]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[3]  Horst Alzer,et al.  Sharp inequalities for the beta function , 2001 .

[4]  D. Varberg.  Convex Functions , 1973 .

[5]  Sever S Dragomir,et al.  SOME INTEGRAL INEQUALITIES OF GR USS TYPE , 1998 .

[6]  Pietro Cerone,et al.  On Some Inequalities Arising from Montgomery's Identity (Montgomery's Identity) , 2000 .

[7]  Pietro Cerone,et al.  ON RELATIONSHIPS BETWEEN OSTROWSKI, TRAPEZOIDAL AND CHEBYCHEV IDENTITIES AND INEQUALITIES , 2001 .

[8]  Pietro Cerone,et al.  On some inequalities for the expectation and variance , 2001 .

[9]  ON SOME GENERALIZATIONS OF STEFFENSEN'S INEQUALITY AND RELATED RESULTS , 2001 .

[10]  Feng Qi,et al.  Lower and upper bounds of ς(3) , 2001 .

[11]  Bai-Ni Guo (郭白妮).  Note on Mathieu's inequality , 2000 .

[12]  Three Point Quadrature Rules , 2002 .

[13]  On Some Results Involving the Čebyšev Functional and its Generalisations , 2002 .

[14]  Themistocles M. Rassias,et al.  Ostrowski type inequalities and applications in numerical integration , 2002 .

[15]  INEQUALITIES RELATED TO THE CHEBYCHEV FUNCTIONAL INVOLVING INTEGRALS OVER DIFFERENT INTERVALS , 2001 .

[16]  Xiao-Liang Cheng,et al.  A NOTE ON THE PERTURBED TRAPEZOID INEQUALITY , 2002 .

[17]  S. Dragomir,et al.  Generalisations of the Grüss, Chebychev and Lupas inequalities for Integrals over Different Intervals , 2000 .

[18]  ON AN IDENTITY FOR THE CHEBYCHEV FUNCTIONAL AND SOME RAMIFICATIONS , 2002 .

[19]  Y. Tong,et al.  Convex Functions, Partial Orderings, and Statistical Applications , 1992 .

[20]  A. M. Fink.  A Treatise on Grüss’ Inequality , 1999 .

[21]  D. S. Mitrinovic,et al.  Classical and New Inequalities in Analysis , 1992 .

[22]  Pietro Cerone,et al.  Three Point Quadrature Rules Involving, at Most, a First Derivative , 1999 .

[23]  P. Cerone,et al.  New upper and lower bounds for the Čebyšev functional. , 2002 .