2<em>D</em> approximately reciprocal <em>ρ</em>-convex functions and associated integral inequalities

Muhammad Uzair Awan; Nousheen Akhtar; Artion Kashuri; Muhammad Aslam Noor; Yu-Ming Chu; Muhammad Uzair Awan; Nousheen Akhtar; Artion Kashuri; Muhammad Aslam Noor; Yu-Ming Chu

doi:10.3934/math.2020299

AIMS Mathematics

2020, Volume 5, Issue 5: 4662-4680. doi: 10.3934/math.2020299

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Research article

2D approximately reciprocal ρ-convex functions and associated integral inequalities

1.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2.
Department of Mathematics, Faculty of Technical Science, University of Vlora “Ismail Qemali”, 9400 Vlorë, Albania
3.
Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
4.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
5.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 02 April 2020 Accepted: 18 May 2020 Published: 27 May 2020
MSC : 26A51, 26D10, 26D15

The main objective of this article is to introduce the notion of 2D approximately reciprocal ρ-convex functions, show that this class of functions unifies several other unrelated classes of reciprocal convex functions, obtain several new refinements of the Hermite-Hadamard type inequalities involving 2D approximately reciprocal ρ-convex functions, provide some bounds pertaining to the trapezium like inequalities by using partial differentiable 2D approximately reciprocal ρ-convex functions, and discuss the special cases of the obtained results.
- convex,
- reciprocal,
- approximately,
- Hermite-Hadamard inequality
Citation: Muhammad Uzair Awan, Nousheen Akhtar, Artion Kashuri, Muhammad Aslam Noor, Yu-Ming Chu. 2D approximately reciprocal ρ-convex functions and associated integral inequalities[J]. AIMS Mathematics, 2020, 5(5): 4662-4680. doi: 10.3934/math.2020299

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Abstract

The main objective of this article is to introduce the notion of 2D approximately reciprocal ρ-convex functions, show that this class of functions unifies several other unrelated classes of reciprocal convex functions, obtain several new refinements of the Hermite-Hadamard type inequalities involving 2D approximately reciprocal ρ-convex functions, provide some bounds pertaining to the trapezium like inequalities by using partial differentiable 2D approximately reciprocal ρ-convex functions, and discuss the special cases of the obtained results.

References

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