Yazar "Ntouyas, Sotiris K." seçeneğine göre listele

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    Fractional Ostrowski type inequalities for differentiable harmonically convex functions
    (Amer Inst Mathematical Sciences-Aims, 2022) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, Hüseyin; Ntouyas, Sotiris K.; Promsakon, Chanon
    In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.
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    Hermite-Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus
    (Mdpi, 2021) Tariboon, Jessada; Ali, Muhammad Aamir; Budak, Huseyin; Ntouyas, Sotiris K.
    In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite-Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.
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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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    POST–QUANTUM OSTROWSKI TYPE INTEGRAL INEQUALITIES FOR TWICE (p,q)–DIFFERENTIABLE FUNCTIONS
    (Element D.O.O., 2022) Luangboon, W.; Nonlaopon, Kamsing; Tariboon, Jessada; Ntouyas, Sotiris K.; Budak, Hüseyin
    In this paper, we establish a new (p,q) -integral identity using twice (p,q) -differentiable functions. Then, we use this result to derive some new post-quantum Ostrowski type integral inequalities for twice (p,q) -differentiable functions. The newly established results are also proven to be generalizations of some existing results in the area of integral inequalities. © 2022, Journal of Mathematical Inequalities. All Rights Reserved.
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    Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions in the second sense with applications
    (Amer Inst Mathematical Sciences-Aims, 2021) Asawasamrit, Suphawat; Ali, Muhammad Aamir; Budak, Huseyin; Ntouyas, Sotiris K.; Tariboon, Jessada
    In this study, we use quantum calculus to prove Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in the second sense. The newly proven results are also shown to be an extension of comparable results in the existing literature. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers.
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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 New Post-Quantum Simpson's Type Inequalities for Coordinated Convex Functions
    (Mdpi, 2022) Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Ntouyas, Sotiris K.; Sarıkaya, Mehmet Zeki; Budak, Hüseyin
    In 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.
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    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 Aamir
    In 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.
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    Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus
    (Mdpi, 2021) Sitho, Surang; Ali, Muhammad Aamir; Budak, Huseyin; Ntouyas, Sotiris K.; Tariboon, Jessada
    In this article, we use quantum integrals to derive Hermite-Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q(x)(2)- quantum integral to show midpoint and trapezoidal inequalities for q(x)(2)-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite- Hadamard-type inequality for preinvex functions via q(x)(1)-quantum integral is not valid for preinvex functions, and we present its proper form. We use q(x)(1)-quantum integrals to show midpoint inequalities for q(x)(1)-differentiable preinvex functions. It is also demonstrated that by considering the limit q -> 1(-) and eta(x(2), x(1)) = -eta(x(1), x(2)) = x(2), x(1) in the newly derived results, the newly proved findings can be turned into certain known results.