Recently, a generalization of convex function called exponentially $ (\alpha, h-m) $-convex function has been introduced. This generalization of convexity is used to obtain upper bounds of fractional integral operators involving Mittag-Leffler (ML) functions. Moreover, the upper bounds of left and right integrals lead to their boundedness and continuity. A modulus inequality is established for differentiable functions. The Hadamard type inequality is proved which shows upper and lower bounds of sum of left and right sided fractional integral operators.
Citation: Maryam Saddiqa, Ghulam Farid, Saleem Ullah, Chahn Yong Jung, Soo Hak Shim. On Bounds of fractional integral operators containing Mittag-Leffler functions for generalized exponentially convex functions[J]. AIMS Mathematics, 2021, 6(6): 6454-6468. doi: 10.3934/math.2021379
Recently, a generalization of convex function called exponentially $ (\alpha, h-m) $-convex function has been introduced. This generalization of convexity is used to obtain upper bounds of fractional integral operators involving Mittag-Leffler (ML) functions. Moreover, the upper bounds of left and right integrals lead to their boundedness and continuity. A modulus inequality is established for differentiable functions. The Hadamard type inequality is proved which shows upper and lower bounds of sum of left and right sided fractional integral operators.
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Maryam Saddiqa, Ghulam Farid, Saleem Ullah, Chahn Yong Jung, Soo Hak Shim. On Bounds of fractional integral operators containing Mittag-Leffler functions for generalized exponentially convex functions[J]. AIMS Mathematics, 2021, 6(6): 6454-6468. doi: 10.3934/math.2021379
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