Advertisement

Error Estimates of Approximations for the Complex Valued Integral Transforms

  • Andrea Aglić AljinovićEmail author
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 151)

Abstract

In this survey paper error estimates of approximations in complex domain for the Laplace and Mellin transform are given for functions f which vanish beyond a finite domain \(\left [ a,b\right ] \subset \left [ 0,\infty \right \rangle \) and whose derivative belongs to \(L_{p}\left [ a,b \right ] \). New inequalities involving integral transform of f, integral mean of f and exponential and logarithmic mean of the endpoints of the domain of f are presented. These estimates enable us to obtain two associated numerical quadrature rules for each transform and error bounds of their remainders.

References

  1. 1.
    A. Aglić Aljinović, Error estimates for approximations of the Laplace transform of functions in L p spaces. Aust. J. Math. Anal. Appl. 8(1), Article 10, 1–22 (2011)Google Scholar
  2. 2.
    A. Aglić Aljinović, Inequalities involving Mellin transform, integral mean, exponential and logarithmic mean. Ann. Univ. Craiova Math. Comput. Sci. Ser. 39(2), 254–264 (2012)MathSciNetzbMATHGoogle Scholar
  3. 3.
    A. Aglić Aljinović, Approximations of the Mellin transform in the complex domain. Adv. Pure Appl. Math. 5(3), 139–149 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Aglić Aljinović, J. Pečarić, I. Perić, Estimates of the difference between two weighted integral means via weighted Montgomery identity. Math. Inequal. Appl. 7(3), 315–336 (2004)MathSciNetzbMATHGoogle Scholar
  5. 5.
    L. Debnath, D. Bhatta, Integral Transforms and Their Applications (Chapman & Hall/CRC, Boca Raton, 2007), 700 pp.zbMATHGoogle Scholar
  6. 6.
    D.S. Mitrinović, J.E. Pečarić, A.M. Fink, Inequalities for Functions and Their Integrals and Derivatives (Kluwer Academic Publishers, Dordrecht, 1994)zbMATHGoogle Scholar
  7. 7.
    J. Pečarić, On the Čebyšev inequality. Bul. Inst. Politehn. Timisoara 25(39), 10–11 (1980)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Zagreb, Faculty of Electrical Engineering and ComputingZagrebCroatia

Personalised recommendations