Error bounds associated with different versions of Hadamard inequalities of mid-point type
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Authors
Muhammad Raees
- School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
Matloob Anwar
- School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
Ghulam Farid
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan.
Abstract
In this paper, we establish the error bounds of different versions of mid-point type inequalities.
At first, we prove two identities for fractional integrals involving the extended generalized
Mittag-Leffler function and generalized exponential fractional integrals, and then we establish the corresponding
error bound inequalities. Furthermore, we find a generalized inequality for error bound
inequalities using a generalized identity. Also, we find some inequalities which formulate all error
bound inequalities for various versions of Hadamard inequality. Finally, we present some examples of
the central moment of a random variable.
Share and Cite
ISRP Style
Muhammad Raees, Matloob Anwar, Ghulam Farid, Error bounds associated with different versions of Hadamard inequalities of mid-point type, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 213--229
AMA Style
Raees Muhammad, Anwar Matloob, Farid Ghulam, Error bounds associated with different versions of Hadamard inequalities of mid-point type. J Math Comput SCI-JM. (2021); 23(3):213--229
Chicago/Turabian Style
Raees, Muhammad, Anwar, Matloob, Farid, Ghulam. "Error bounds associated with different versions of Hadamard inequalities of mid-point type." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 213--229
Keywords
- Convex function
- extended generalized Mittag-Leffler function
- generalized integral
- Hadamard inequality
MSC
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