New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions

Muhammad Aamir Ali, Fongchan Wannalookkhee, Hüseyin Budak, Sina Etemad () and Shahram Rezapour ()
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Muhammad Aamir Ali: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Fongchan Wannalookkhee: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Hüseyin Budak: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Shahram Rezapour: Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam

Mathematics, 2022, vol. 10, issue 19, 1-24

Abstract: In both pure and applied mathematics, convex functions are used in many different problems. They are crucial to investigate both linear and non-linear programming issues. Since a convex function is one whose epigraph is a convex set, the theory of convex functions falls under the umbrella of convexity. However, it is a significant theory that affects practically all areas of mathematics. In this paper, we introduce the notions of g , h -convexity or convexity with respect to a pair of functions on co-ordinates and discuss its fundamental properties. Moreover, we establish some novel Hermite–Hadamard- and Ostrowski-type inequalities for newly introduced co-ordinated convexity. Additionally, it is presented that the newly introduced notion of the convexity and given inequalities are generalizations of existing studies in the literature. Lastly, we look at various mathematical examples and graphs to confirm the validity of the newly found inequalities.

Keywords: Hermite–Hadamard inequality; Ostrowski inequalities; convex functions; co-ordinated convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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