TY - JOUR T1 - Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms AU - Albayrak, Durmuş PY - 2024 DA - April Y2 - 2024 DO - 10.36753/mathenot.1362335 JF - Mathematical Sciences and Applications E-Notes JO - Math. Sci. Appl. E-Notes PB - Murat TOSUN WT - DergiPark SN - 2147-6268 SP - 81 EP - 92 VL - 12 IS - 2 LA - en AB - 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. KW - Generalized Laplace transform KW - Generalized Stieltjes transform KW - Laplace transform KW - Parseval-Goldstein theorem CR - [1] Debnath, L., Bhatta, D.: Integral Transforms and Their Applications(3rd ed.). Chapman and Hall/CRC. 2014. CR - [2] Yürekli, O.: A Parseval-type theorem applied to certain integral transforms. IMA Journal of Applied Mathematics. 42 (3), 241-249 (1989). CR - [3] Yürekli, O.: A theorem on the generalized Stieltjes transform, Journal of Mathematical Analysis and Applications. 168(1), 63-71 (1992). CR - [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). CR - [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). CR - [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). CR - [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). CR - [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). CR - [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). CR - [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). CR - [11] Dzhrbashyan, M. M.: Integral Transforms and Representations of Functions in the Complex Domain. Nauka, Moscow. 1966. CR - [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. CR - [13] Widder, D. V.: A transform related to the Poisson integral for a half-plane. Duke Mathematical Journal. 33 (2), 355–362 (1966). CR - [14] Glasser, M. L.: Some Bessel function integrals. Kyungpook Mathematical Journal. 13 (2), 171–174 (1973). CR - [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). CR - [16] Oldham, K. B., Spanier, J., Myland, J.: An Atlas of Functions. Springer. 2010. CR - [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. CR - [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). UR - https://doi.org/10.36753/mathenot.1362335 L1 - https://dergipark.org.tr/en/download/article-file/3416313 ER -