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Öğe New Hermite-Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions(Mdpi, 2022) Ali, Muhammad Aamir; Wannalookkhee, Fongchan; Budak, Hüseyin; Etemad, Sina; Rezapour, ShahramIn 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.Öğe On some new quantum trapezoid-type inequalities for q-differentiable coordinated convex functions(Institute for Ionics, 2023) Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Sarikaya, M.Z.; Budak, Hüseyin; Ali, Muhammad AamirIn this paper, we establish several new inequalities for q-differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We also show that the inequalities proved in this paper generalize the results given in earlier works. Moreover, we give some examples in order to demonstrate our main results. © 2023, The Author(s).Öğe Post quantum Ostrowski-type inequalities for coordinated convex functions(Wiley, 2022) Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Ntouyas, Sortiris K.; Budak, HüseyinIn this article, we give a new notion of (p, q) derivatives for continuous functions on coordinates. We also derive post quantum Ostrowski-type inequalities for coordinated convex functions. Our significant results are considered as the generalizations of other results that appeared in the literature.Öğe Some New Post-Quantum Simpson's Type Inequalities for Coordinated Convex Functions(Mdpi, 2022) Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Ntouyas, Sotiris K.; Sarıkaya, Mehmet Zeki; Budak, HüseyinIn this paper, we establish some new Simpson's type inequalities for coordinated convex functions by using post-quantum calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works.Öğe Some New Quantum Hermite-Hadamard Inequalities for Co-Ordinated Convex Functions(Mdpi, 2022) Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Ntouyas, Sotiris K.; Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Ali, Muhammad AamirIn this paper, we establish some new versions of Hermite-Hadamard type inequalities for co-ordinated convex functions via q(1),q(2)-integrals. Since the inequalities are newly proved, we therefore consider some examples of co-ordinated convex functions and show their validity for particular choices of q(1),q(2) is an element of(0,1). We hope that the readers show their interest in these results.Öğe Some Quantum Integral Inequalities for (p, h)-Convex Functions(Mdpi, 2023) Kantalo, Jirawat; Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Budak, HüseyinIn this paper, we derive an identity of the q-definite integral of a continuous function f on a finite interval. We then use such identity to prove some new quantum integral inequalities for (p,h)-convex function. The results obtained in this paper generalize previous work in the literature.
