Yazar "Vivas-Cortez, Miguel" seçeneğine göre listele

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    Advances in Ostrowski-Mercer Like Inequalities within Fractal Space
    (Mdpi, 2023) Vivas-Cortez, Miguel; Awan, Muhammad Uzair; Asif, Usama; Javed, Muhammad Zakria; Budak, Hueseyin
    The main idea of the current investigation is to explore some new aspects of Ostrowski's type integral inequalities implementing the generalized Jensen-Mercer inequality established for generalized s-convexity in fractal space. To proceed further with this task, we construct a new generalized integral equality for first-order local differentiable functions, which will serve as an auxiliary result to restore some new bounds for Ostrowski inequality. We establish our desired results by employing the equality, some renowned generalized integral inequalities like Holder's, power mean, Yang-Holder's, bounded characteristics of the functions and considering generalized s-convexity characteristics of functions. Also, in support of our main findings, we deliver specific applications to means, and numerical integration and graphical visualization are also presented here.
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    Generalizations of fractional Hermite-Hadamard-Mercer like inequalities for convex functions
    (Amer Inst Mathematical Sciences-Aims, 2021) Vivas-Cortez, Miguel; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin
    In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, k-Riemann-Liouville (k-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel.
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    New version of midpoint-type inequalities for co-ordinated convex functions via generalized conformable integrals
    (Springer, 2024) Kiris, Mehmet Eyup; Vivas-Cortez, Miguel; Uzun, Tugba Yalcin; Bayrak, Gozde; Budak, Hüseyin
    In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann-Liouville fractional integrals and Riemann integrals.
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    On Fractional Ostrowski-Mercer-Type Inequalities and Applications
    (Mdpi, 2023) Ramzan, Sofia; Awan, Muhammad Uzair; Vivas-Cortez, Miguel; Budak, Hueseyin
    The objective of this research is to study in detail the fractional variants of Ostrowski-Mercer-type inequalities, specifically for the first and second order differentiable s-convex mappings of the second sense. To obtain the main outcomes of the paper, we leverage the use of conformable fractional integral operators. We also check the numerical validations of the main results. Our findings are also validated through visual representations. Furthermore, we provide a detailed discussion on applications of the obtained results related to special means, q-digamma mappings, and modified Bessel mappings.
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    On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals
    (Amer Inst Mathematical Sciences-Aims, 2024) Kiris, Mehmet Eyup; Vivas-Cortez, Miguel; Bayrak, Gozde; Cmar, Tugba; Budak, Hüseyin
    In this study, some new Hermite-Hadamard type inequalities for co-ordinated convex functions were obtained with the help of conformable fractional integrals. We have presented some remarks to give the relation between our results and earlier obtained results. Moreover, an identity for partial differentiable functions has been established. By using this equality and concept of co-ordinated convexity, we have proven a trapezoid type inequality for conformable fractional integrals.
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    Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function
    (Taylor & Francis Inc, 2024) Munir, Arslan; Vivas-Cortez, Miguel; Qayyum, Ather; Budak, Hüseyin; Faiz, Irza; Supadi, Siti Suzlin
    Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for $s$s-convex function are obtained. By employing well-known inequalities such as H & ouml;lder's and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.
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    Some New Hermite-Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
    (Mdpi, 2021) Vivas-Cortez, Miguel; Ali, Muhammad Aamir; Budak, Hüseyin; Kalsoom, Humaira; Agarwal, Praveen
    In this investigation, for convex functions, some new (p,q)-Hermite-Hadamard-type inequalities using the notions of (p,q)(pi 2) derivative and (p,q)(pi 2) integral are obtained. Furthermore, for (p,q)(pi 2)-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)(pi 2) integral are offered. It is also shown that the newly proved results for p=1 and q -> 1(-) can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
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    A Study Of Fractional Hermite-Hadamard-Mercer Inequalities For Differentiable Functions
    (World Scientific Publ Co Pte Ltd, 2024) Sitthiwirattham, Thanin; Vivas-Cortez, Miguel; Ali, Muhammad aamir; Budak, Hüseyin; Avci, Ibrahim
    In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite-Hadamard-Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson's type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs.