Yazar "Rezapour, Shahram" seçeneğine göre listele

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    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, Shahram
    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.
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    A new version of (p, q)-Hermite-Hadamard's midpoint and trapezoidal inequalities via special operators in (p, q)-calculus
    (Springer, 2022) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, Hüseyin; Etemad, Sina; Rezapour, Shahram
    In this paper, we conduct a research on a new version of the (p, q)-Hermite-Hadamard inequality for convex functions in the framework of postquantum calculus. Moreover, we derive several estimates for (p, q)-midpoint and (p, q)-trapezoidal inequalities for special (p, q)-differentiable functions by using the notions of left and right (p, q)-derivatives. Our newly obtained inequalities are extensions of some existing inequalities in other studies. Lastly, we consider some mathematical examples for some (p, q)-functions to confirm the correctness of newly established results.
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    A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators
    (Hindawi Ltd, 2023) Kara, Hasan; Budak, Hueseyin; Etemad, Sina; Rezapour, Shahram; Ahmad, Hijaz; Kaabar, Mohammed K. A.
    This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Holder's inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.