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Year 2024, Volume: 12 Issue: 2, 81 - 92, 14.04.2024
https://doi.org/10.36753/mathenot.1362335

Abstract

References

  • [1] Debnath, L., Bhatta, D.: Integral Transforms and Their Applications(3rd ed.). Chapman and Hall/CRC. 2014.
  • [2] Yürekli, O.: A Parseval-type theorem applied to certain integral transforms. IMA Journal of Applied Mathematics. 42 (3), 241-249 (1989).
  • [3] Yürekli, O.: A theorem on the generalized Stieltjes transform, Journal of Mathematical Analysis and Applications. 168(1), 63-71 (1992).
  • [4] Albayrak, D., Dernek, N.: Some relations for the generalized e Gn; e Pn integral transforms and Riemann-Liouville, Weyl integral operators. Gazi University Journal of Science. 36 (1), 362-381 (2023).
  • [5] Albayrak, D., Dernek, N.: On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics. 50 (2), 526-540 (2021).
  • [6] Karataş, H. B., Kumar, D., Uçar, F.: Some iteration and Parseval-Goldstein type identities with their applications. Advances in Mathematical Sciences and Applications. 29 (2), 563–574 (2020).
  • [7] Karataş, H. B., Albayrak, D., Uçar, F.: Some Parseval-Goldstein type identities with illustrative examples. Proceedings of the Institute of Mathematics and Mechanics. 49 (1), 60-68 (2023).
  • [8] Albayrak, D.: Theory and applications on a new generalized Laplace-type integral transform. Mathematical Methods in the Applied Sciences. 46 (4), 4363-4378 (2023).
  • [9] Yürekli, O., Sadek, I.: A Parseval Goldstein type theorem on the Widder potential and its applications. International Journal of Mathematics and Mathematical Sciences. 14, 160375, 517-524 (1991).
  • [10] Al-Musallam, F., Kiryakova, V., Tuan, V. K.: A multi-index Borel-Dzrbashjan transform. Rocky Mountain Journal of Mathematics. 32 (2), 409–428 (2002).
  • [11] Dzhrbashyan, M. M.: Integral Transforms and Representations of Functions in the Complex Domain. Nauka, Moscow. 1966.
  • [12] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. Vol. II. New York- Toronto-London. McGraw-Hill Book Company. Inc. 1954.
  • [13] Widder, D. V.: A transform related to the Poisson integral for a half-plane. Duke Mathematical Journal. 33 (2), 355–362 (1966).
  • [14] Glasser, M. L.: Some Bessel function integrals. Kyungpook Mathematical Journal. 13 (2), 171–174 (1973).
  • [15] Dernek, N., Kurt, V., ¸Sim¸sek, Y., Yürekli, O.: A generalization of the Widder potential transform and applications. Integral Transforms and Special Functions. 22 (6), 391-401 (2011).
  • [16] Oldham, K. B., Spanier, J., Myland, J.: An Atlas of Functions. Springer. 2010.
  • [17] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. Vol. I. New York- Toronto-London. McGraw-Hill Book Company. Inc. 1954.
  • [18] Ferreira, J., Salinas, S.: A gamma type distribution involving a confluent hypergeometric function of the second kind. Revista Técnica de la Facultad de Ingeniería Universidad del Zulia. 33 (2), 169-175 (2010).

Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms

Year 2024, Volume: 12 Issue: 2, 81 - 92, 14.04.2024
https://doi.org/10.36753/mathenot.1362335

Abstract

In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we evaluated improper integrals of some fundamental and special functions using our results.

References

  • [1] Debnath, L., Bhatta, D.: Integral Transforms and Their Applications(3rd ed.). Chapman and Hall/CRC. 2014.
  • [2] Yürekli, O.: A Parseval-type theorem applied to certain integral transforms. IMA Journal of Applied Mathematics. 42 (3), 241-249 (1989).
  • [3] Yürekli, O.: A theorem on the generalized Stieltjes transform, Journal of Mathematical Analysis and Applications. 168(1), 63-71 (1992).
  • [4] Albayrak, D., Dernek, N.: Some relations for the generalized e Gn; e Pn integral transforms and Riemann-Liouville, Weyl integral operators. Gazi University Journal of Science. 36 (1), 362-381 (2023).
  • [5] Albayrak, D., Dernek, N.: On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics. 50 (2), 526-540 (2021).
  • [6] Karataş, H. B., Kumar, D., Uçar, F.: Some iteration and Parseval-Goldstein type identities with their applications. Advances in Mathematical Sciences and Applications. 29 (2), 563–574 (2020).
  • [7] Karataş, H. B., Albayrak, D., Uçar, F.: Some Parseval-Goldstein type identities with illustrative examples. Proceedings of the Institute of Mathematics and Mechanics. 49 (1), 60-68 (2023).
  • [8] Albayrak, D.: Theory and applications on a new generalized Laplace-type integral transform. Mathematical Methods in the Applied Sciences. 46 (4), 4363-4378 (2023).
  • [9] Yürekli, O., Sadek, I.: A Parseval Goldstein type theorem on the Widder potential and its applications. International Journal of Mathematics and Mathematical Sciences. 14, 160375, 517-524 (1991).
  • [10] Al-Musallam, F., Kiryakova, V., Tuan, V. K.: A multi-index Borel-Dzrbashjan transform. Rocky Mountain Journal of Mathematics. 32 (2), 409–428 (2002).
  • [11] Dzhrbashyan, M. M.: Integral Transforms and Representations of Functions in the Complex Domain. Nauka, Moscow. 1966.
  • [12] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. Vol. II. New York- Toronto-London. McGraw-Hill Book Company. Inc. 1954.
  • [13] Widder, D. V.: A transform related to the Poisson integral for a half-plane. Duke Mathematical Journal. 33 (2), 355–362 (1966).
  • [14] Glasser, M. L.: Some Bessel function integrals. Kyungpook Mathematical Journal. 13 (2), 171–174 (1973).
  • [15] Dernek, N., Kurt, V., ¸Sim¸sek, Y., Yürekli, O.: A generalization of the Widder potential transform and applications. Integral Transforms and Special Functions. 22 (6), 391-401 (2011).
  • [16] Oldham, K. B., Spanier, J., Myland, J.: An Atlas of Functions. Springer. 2010.
  • [17] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. Vol. I. New York- Toronto-London. McGraw-Hill Book Company. Inc. 1954.
  • [18] Ferreira, J., Salinas, S.: A gamma type distribution involving a confluent hypergeometric function of the second kind. Revista Técnica de la Facultad de Ingeniería Universidad del Zulia. 33 (2), 169-175 (2010).
There are 18 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Durmuş Albayrak 0000-0002-3786-5900

Early Pub Date January 29, 2024
Publication Date April 14, 2024
Submission Date September 18, 2023
Acceptance Date January 24, 2024
Published in Issue Year 2024 Volume: 12 Issue: 2

Cite

APA Albayrak, D. (2024). Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms. Mathematical Sciences and Applications E-Notes, 12(2), 81-92. https://doi.org/10.36753/mathenot.1362335
AMA Albayrak D. Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms. Math. Sci. Appl. E-Notes. April 2024;12(2):81-92. doi:10.36753/mathenot.1362335
Chicago Albayrak, Durmuş. “Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms”. Mathematical Sciences and Applications E-Notes 12, no. 2 (April 2024): 81-92. https://doi.org/10.36753/mathenot.1362335.
EndNote Albayrak D (April 1, 2024) Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms. Mathematical Sciences and Applications E-Notes 12 2 81–92.
IEEE D. Albayrak, “Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms”, Math. Sci. Appl. E-Notes, vol. 12, no. 2, pp. 81–92, 2024, doi: 10.36753/mathenot.1362335.
ISNAD Albayrak, Durmuş. “Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms”. Mathematical Sciences and Applications E-Notes 12/2 (April 2024), 81-92. https://doi.org/10.36753/mathenot.1362335.
JAMA Albayrak D. Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms. Math. Sci. Appl. E-Notes. 2024;12:81–92.
MLA Albayrak, Durmuş. “Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms”. Mathematical Sciences and Applications E-Notes, vol. 12, no. 2, 2024, pp. 81-92, doi:10.36753/mathenot.1362335.
Vancouver Albayrak D. Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms. Math. Sci. Appl. E-Notes. 2024;12(2):81-92.

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