Yazar "Nonlaopon, Kamsing" seçeneğine göre listele

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    New Quantum Mercer Estimates of Simpson-Newton-like Inequalities via Convexity
    (Mdpi, 2022) Butt, Saad Ihsan; Budak, Hüseyin; Nonlaopon, Kamsing
    Recently, developments and extensions of quadrature inequalities in quantum calculus have been extensively studied. As a result, several quantum extensions of Simpson's and Newton's estimates are examined in order to explore different directions in quantum studies. The main motivation of this article is the development of variants of Simpson-Newton-like inequalities by employing Mercer's convexity in the context of quantum calculus. The results also give new quantum bounds for Simpson-Newton-like inequalities through Holder's inequality and the power mean inequality by employing the Mercer scheme. The validity of our main results is justified by providing examples with graphical representations thereof. The obtained results recapture the discoveries of numerous authors in quantum and classical calculus. Hence, the results of these inequalities lead us to the development of new perspectives and extensions of prior results.
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    New Variants of Quantum Midpoint-Type Inequalities
    (Mdpi, 2022) Butt, Saad Ihsan; Budak, Hüseyin; Nonlaopon, Kamsing
    Recently, there has been a strong push toward creating and expanding quadrature inequalities in quantum calculus. In order to investigate various avenues for quantum inquiry, a number of quantum extensions of midpoint estimations are studied. The goal of this research article is to discover novel quantum midpoint-type inequalities that are twice q(xi 2)-differentiable for (alpha,m)-convex functions. Firstly, we obtain novel identity for q(xi 2)-integral by employing quantum calculus tools. Then by using the auxiliary identity, we formulate new bounds by taking into account the known quantum Holder and Power mean inequalities. An example is provided with a graphical representation to show the validity of obtaining results. The outcomes of this study clarify and expand earlier research on midpoint-type inequalities. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.
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    Newton-type inequalities associated with convex functions via quantum calculus
    (Univ Miskolc Inst Math, 2024) Luangboon, Waewta; Nonlaopon, Kamsing; Sarikaya, Mehmet Zeki; Budak, Huseyin
    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 Fractional Newton Inequalities via Coordinated Convex Functions
    (Mdpi, 2022) Kösem, Pınar; Kara, Hasan; Budak, Hüseyin; Ali, Muhammad Aamir; Nonlaopon, Kamsing
    In this paper, firstly, we present an integral identity for functions of two variables via Riemann-Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are obtained with the aid of the Holder and power mean inequality. In addition, we investigate some Newton-type inequalities utilizing mappings of two variables with bounded variation. Finally, we gave some mathematical examples and their graphical behavior to validate the obtained 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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    On generalizations of trapezoid and Bullen type inequalities based on generalized fractional integrals
    (Amer Inst Mathematical Sciences-Aims, 2022) Budak, Hüseyin; Ertuğral, Fatma; Ali, Muhammad Aamir; Bilişik, Özge Nalan; Sarıkaya, Mehmet Zeki; Nonlaopon, Kamsing
    In this paper, we establish an integral identity involving differentiable functions and generalized fractional integrals. Then, using the newly established identity, we prove some new general versions of Bullen and trapezoidal type inequalities for differentiable convex functions. The main benefit of the newly established inequalities is that they can be converted into similar inequalities for classical integrals, Riemann-Liouville fractional integrals, k-Riemann-Liouville fractional integrals, Hadamard fractional integrals, etc. Moreover, the inequalities presented in the paper are extensions of several existing inequalities in the literature.
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    On Hermite-Hadamard-Fejer-Type Inequalities for ?-Convex Functions via Quantum Calculus
    (Mdpi, 2023) Arunrat, Nuttapong; Nonlaopon, Kamsing; Budak, Hueseyin
    In this paper, we use qa- and qb-integrals to establish some quantum Hermite-Hadamard-Fejer-type inequalities for ?-convex functions. By taking q & RARR;1, our results reduce to classical results on Hermite-Hadamard-Fejer-type inequalities for ?-convex functions. Moreover, we give some examples for quantum Hermite-Hadamard-Fejer-type inequalities for ?-convex functions. Some results presented here for ?-convex functions provide extensions of others given in earlier works for convex and ?-convex functions.
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    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 Aamir
    In 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).
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    Parametric generalized (p, q)-integral inequalities and applications
    (Amer Inst Mathematical Sciences-Aims, 2022) Nonlaopon, Kamsing; Awan, Muhammad Uzair; Talib, Sadia; Budak, Hüseyin
    A new generalized (p, q)-integral identity is derived. Using this new identity as an auxiliary result, we derive new parametric generalizations of certain integral inequalities using the class of s-preinvex functions. We discuss several new and known special cases of the obtained results. This shows that our results are quite unifying. To demonstrate the significance of the main results, we also present some interesting applications.
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    Post quantum Ostrowski-type inequalities for coordinated convex functions
    (Wiley, 2022) Wannalookkhee, Fongchan; Nonlaopon, Kamsing; Ntouyas, Sortiris K.; Budak, Hüseyin
    In 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.
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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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    A Quantum Calculus View of Hermite-Hadamard-Jensen-Mercer Inequalities with Applications
    (Mdpi, 2022) Bin Mohsin, Bandar; Saba, Mahreen; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Budak, Hüseyin; Nonlaopon, Kamsing
    In this paper, we derive some new quantum estimates of generalized Hermite-Hadamard-Jensen-Mercer type of inequalities, essentially using q-differentiable convex functions. With the help of numerical examples, we check the validity of the results. We also discuss some special cases which show that our results are quite unifying. To show the efficiency of our main results, we offer some interesting applications to special means.
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    Riemann-Liouville Fractional Newton's Type Inequalities for Differentiable Convex Functions
    (Mdpi, 2022) Sitthiwirattham, Thanin; Nonlaopon, Kamsing; Ali, Muhammad Aamir; Budak, Hüseyin
    In this paper, we prove some new Newton's type inequalities for differentiable convex functions through the well-known Riemann-Liouville fractional integrals. Moreover, we prove some inequalities of Riemann-Liouville fractional Newton's type for functions of bounded variation. It is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. Finally, we give some examples with graphs and show the validity of newly established inequalities.
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    Simpson's and Newton's Type Inequalities for (alpha, m)-Convex Functions via Quantum Calculus
    (Mdpi, 2022) Soontharanon, Jarunee; Ali, Muhammad Aamir; Budak, Hüseyin; Nonlaopon, Kamsing; Abdullah, Zoya
    In this paper, we give the generalized version of the quantum Simpson's and quantum Newton's formula type inequalities via quantum differentiable (alpha, m)-convex functions. The main advantage of these new inequalities is that they can be converted into quantum Simpson and quantum Newton for convex functions, Simpson's type inequalities (alpha, m)-convex function, and Simpson's type inequalities without proving each separately. These inequalities can be helpful in finding the error bounds of Simpson's and Newton's formulas in numerical integration. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.
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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.
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    Some New Generalized Fractional Newton's Type Inequalities for Convex Functions
    (Hindawi Ltd, 2022) Soontharanon, Jarunee; Ali, Muhammad Aamir; Budak, Hüseyin; Kösem, Pınar; Nonlaopon, Kamsing; Sitthiwirattham, Thanin
    In this paper, we establish some new Newton's type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k-fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature.
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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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    Some New Quantum Hermite-Hadamard Type Inequalities for s-Convex Functions
    (Mdpi, 2022) Gulshan, Ghazala; Budak, Hüseyin; Hussain, Rashida; Nonlaopon, Kamsing
    In this investigation, we first establish new quantum Hermite-Hadamard type integral inequalities for s-convex functions by utilizing newly defined T-q-integrals. Then, by using obtained inequality, we establish a new Hermite-Hadamard inequality for coordinated (s(1), s(2))-convex functions. The results obtained in this paper provide significant extensions of other related results given in the literature. Finally, some examples are given to illustrate the result obtained in this paper. These types of analytical inequalities, as well as solutions, apply to different areas where the concept of symmetry is important.