Yazar "Luangboon, Waewta" seçeneğine göre listele

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    Newton-type inequalities associated with convex functions via quantum calculus
    (Univ Miskolc Inst Math, 2024) Luangboon, Waewta; Nonlaopon, Kamsing; Sarıkaya, Mehmet Zeki; Budak, Hüseyin
    In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton -type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking q -> 1(-) . Finally, we give mathematical examples of convex functions to verify the newly established inequalities.
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    On generalizations of some integral inequalities for preinvex functions via (p, q)-calculus
    (Springer, 2022) Luangboon, Waewta; Nonlaopon, Kamsing; Tariboon, Jessada; Ntouyas, Sotiris K.; Budak, Hüseyin
    In this paper, we establish some new (p, q)-integral inequalities of Simpson's second type for preinvex functions. Many results given in this paper provide generalizations and extensions of the results given in previous research. Moreover, some examples are given to illustrate the investigated results.
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    Some (p, q)-Integral Inequalities of Hermite-Hadamard Inequalities for (p, q)-Differentiable Convex Functions
    (Mdpi, 2022) Luangboon, Waewta; Nonlaopon, Kamsing; Tariboon, Jessada; Ntouyas, Sotiris K.; Budak, Hüseyin
    In this paper, we establish a new (p,q)(b)-integral identity involving the first-order (p,q)(b)-derivative. Then, we use this result to prove some new (p,q)(b)-integral inequalities related to Hermite-Hadamard inequalities for (p,q)(b)-differentiable convex functions. Furthermore, our main results are used to study some special cases of various integral inequalities. The newly presented results are proven to be generalizations of some integral inequalities of already published results. Finally, some examples are given to illustrate the investigated results.
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    Some Generalizations of Different Types of Quantum Integral Inequalities for Differentiable Convex Functions with Applications
    (Mdpi, 2022) Zhao, Dafang; Ali, Muhammad Aamir; Luangboon, Waewta; Budak, Hüseyin; Nonlaopon, Kamsing
    In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson's type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results.