Abstract
Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use Ï-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric Ï-convex functions in the form of a Hadamard inequality. Also, for Ï-convex functions, we obtain bounds of different known fractional and conformable fractional integrals. The results of this paper are applicable to convex functions.
Highlights
Introduction and preliminariesSome very interesting properties of convex functions make them important in mathematical analysis
It should be noted that in new problems related to convexity, generalized assumptions about convex functions are necessary to obtain applicable results
Many important generalizations can be found for convex functions, such as α-convex, m-convex, h-convex, (α, m)-convex, (h, m)-convex, s-convex, (s, m)-convex, GA-convex, GG-convex, and preinvex functions [1, 3, 5, 9, 11, 13, 14, 17, 18, 20, 24]
Summary
Introduction and preliminariesSome very interesting properties of convex functions make them important in mathematical analysis. 2, we use Ï-convex functions to obtain bounds of integral operators given in Definition 6. We get some particular bounds by the Ï-convexity of |f | and defining a convenient integral operator of convolution of two functions.
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