Petrović-Type Inequalities for Harmonic h-convex Functions

By Imran Abbas Baloch, Y. Chu. 2020

55 citations recorded by the source corpus.

In the article, we establish several Petrovic-type inequalities for the harmonic - convex (concave) function if is a submultiplicative (super-multiplicative) function, provide some new majorizaton type inequalities for harmonic convex function, and prove the superadditivity, subadditivity, linearity, and monotonicity properties for the functionals derived from the Petrovic type inequalities.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/181a383fb180b9833c1920e42b3ab6a2c44d146e

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Ostrowski type inequalities in the sense of generalized $\mathcal{K}$-fractional integral operator for exponentially convex functions (2020, background): “For observing various other kinds of exponentially convex functions and their generalizations, see [1,2,6,7,10,12,40,54,66,67].”
Conformable fractional integral inequalities for GG- and GA-convex functions (2020, background): “5013 Recently, many generalizations, invariants and extensions have been made for the convexity, for example, harmonic-convexity [21,22], exponential-convexity [23,24], s-convexity [25,26], Schur-convexity [27–29], strong convexity [30–33], Hp,q-convexity [34–38], generalized convexity [39], GG- and”
Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “The complete elliptic integral K(r) (0 < r < 1) [1,7,8,11,23,27,32,39,40,43,46,48,51] of the first kind is closely related to the complete elliptic integral E(r) of the second kind, which is defined by”
Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind (2020, background): “have been found that they have many important applications in mathematics as well as in physics and engineering, including the evaluation of the length of curves [1, 5, 9, 10, 22, 28, 39, 42, 46, 55], the algorithm of the circumference ration π [11, 13, 21, 41], the computations of electromagnetic f”