The growth and approximation for an analytic function represented by Laplace-Stieltjes transforms with generalized order converging in the half plane.
JOURNAL OF INEQUALITIES AND APPLICATIONS 2018;
2018:185. [PMID:
30137913 PMCID:
PMC6062488 DOI:
10.1186/s13660-018-1783-y]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Accepted: 07/18/2018] [Indexed: 06/08/2023]
Abstract
By utilizing the concept of generalized order, we investigate the growth of Laplace-Stieltjes transform converging in the half plane and obtain one equivalence theorem concerning the generalized order of Laplace-Stieltjes transforms. Besides, we also study the problem on the approximation of this Laplace-Stieltjes transform and give some results about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms. Our results are extension and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.
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