A Certain Class of Weighted Approximations for Integrable Functions and Applications

REFERENCES

• X.-L. Cheng ( 2001 ). Improvement of some Ostrowski-Gruss type inequalities . Comput. Math. Appl. 42 : 109 – 114 .
   Web of Science ®Google Scholar
• S. S. Dragomir and S. Wang ( 1997 ). An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules . Comput. Math. Appl. 33 : 15 – 20 .
   Web of Science ®Google Scholar
• W. Gautschi ( 1997 ). Numerical Analysis: An Introduction . Birkhauser , Boston .
   Google Scholar
• G. Gruss ( 1935 ). Uber das Maximum des absoluten Betrages von . Math. Z. 39 : 215 – 226 .
   Google Scholar
• Z. Liu ( 2007 ). Some Ostrowski-Gruss type inequalities and applications . Comput. Math. Appl. 53 : 73 – 79 .
   Web of Science ®Google Scholar
• M. Masjed-Jamei ( 2011 ). A linear constructive approximation for integrable functions and a parametric quadrature model based on a generalization of Ostrowski Gruss type inequalities . Elect. Trans. Numer. Anal. 38 : 218 – 232 .
   Web of Science ®Google Scholar
• M. Masjed-Jamei , G. V. Milovanovic , and M. A. Jafari ( 2011 ). Explicit forms of weighted quadrature rules with geometric nodes . Math. Comput. Model. 53 : 1133 – 1139 .
   Web of Science ®Google Scholar
• M. Masjed-Jamei , G. V. Milovanovic , and M. A. Jafari (to appear). Closed Expressions for Coefficients in Weighted Newton-Cotes Quadratures, Filomat .
   Google Scholar
• G. V. Milovanovic and A. S. Cvetkovic ( 2010 ). Nonstandard Gaussian quadrature formulae based on operator values . Adv. Comput. Math. 32 : 431 – 486 .
   Web of Science ®Google Scholar
• D. S. Mitrinovic , J. E. Pecaric , and A. M. Fink ( 1993 ). Classical and New Inequalities in Analysis , Kluwer Academic Publishers , Dordrecht .
   Google Scholar
• A. Ostrowski ( 1938 ). Uber die absolutabweichung einer differentiebaren funktion van ihrem integralmittelwert . Comment Math. Helv. 10 : 226 – 227 .
   Google Scholar