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Öğe A Comprehensive Analysis of Hermite-Hadamard Type Inequalities via Generalized Preinvex Functions(Mdpi, 2021) Tariq, Muhammad; Ahmad, Hijaz; Budak, Hüseyin; Sahoo, Soubhagya Kumar; Sitthiwirattham, Thanin; Reunsumrit, JirapornThe principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known Hermite-Hadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field.Öğe Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions(Univ Miskolc Inst Math, 2023) Ali, Muhammad Aamir; Soontharanon, Jarunee; Budak, Hüseyin; Sitthiwirattham, Thanin; Feckan, MichalIn this article, we establish two new and different versions of fractional HermiteHadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Ho & BULL;lder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.Öğe Fractional Hermite-Hadamard inequality, Simpson's and Ostrowski's type inequalities for convex functions with respect to a pair of functions(Rocky Mt Math Consortium, 2023) Xie, Jianqiang; Ali, Muhammad Aamir; Budak, Hüseyin; Feckan, Michal; Sitthiwirattham, ThaninWe consider the convexity with respect to a pair of functions and establish a Hermite-Hadamard type inequality for Riemann-Liouville fractional integrals. Moreover, we derive some new Simpson's and Ostrowski's type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.Öğe 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, ChanonIn 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.Öğe Hermite-Hadamard-Mercer-Type Inequalities for Harmonically Convex Mappings(Mdpi, 2021) You, Xuexiao; Ali, Muhammad Aamir; Budak, Hüseyin; Reunsumrit, Jiraporn; Sitthiwirattham, ThaninIn this paper, we prove Hermite-Hadamard-Mercer inequalities, which is a new version of the Hermite-Hadamard inequalities for harmonically convex functions. We also prove Hermite-Hadamard-Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.Öğe A new Q-Hermite-Hadamard's inequality and estimates for midpoint type inequalities for convex functions(Univ Miskolc Inst Math, 2023) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Ali, Asghar; Budak, HüseyinThis paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals. We also prove some new midpoint-type inequalities for q-differentiable con-vex functions. Moreover, we present some examples to illustrate our established results, supple-mented with graphs.Öğe A new variant of Jensen inclusion and Hermite-Hadamard type inclusions for interval-valued functions(University of Nis, 2023) Sitthiwirattham, Thanin; Sial, I.B.; Ali, Muhammad Aamir; Budak, Hüseyin; Reunsumrit, J.In this research, we give a new version of Jensen inclusion for interval-valued functions, which is called Jensen-Mercer inclusion. Moreover, we establish some new inclusions of the Hermite-Hadamard-Mercer type for interval-valued functions. Finally, we give some applications of newly established inequalities to make them more interesting for the readers. © 2023, University of Nis. All rights reserved.Öğe 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, ShahramIn 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.Öğe On generalizations of quantum Simpson's and quantum Newton's inequalities with some parameters(Amer Inst Mathematical Sciences-Aims, 2021) Promsakon, Chanon; Ali, Muhammad Aamir; Budak, Hüseyin; Abbas, Mujahid; Muhammad, Faheem; Sitthiwirattham, ThaninIn this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson's and Newton's type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.Öğe On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables(Mdpi, 2021) Sitthiwirattham, Thanin; Budak, Hüseyin; Kara, Hasan; Ali, Muhammad Aamir; Reunsumrit, JirapornIn this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann-Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.Öğe On Some New Maclaurin's Type Inequalities for Convex Functions in q-Calculus(Mdpi, 2023) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, HüseyinThis work establishes some new inequalities to find error bounds for Maclaurin's formulas in the framework of q-calculus. For this, we first prove an integral identity involving q-integral and q-derivative. Then, we use this new identity to prove some q-integral inequalities for q-differentiable convex functions. The inequalities proved here are very important in the literature because, with their help, we can find error bounds for Maclaurin's formula in both q and classical calculus.Öğe On Some New Ostrowski-Mercer-Type Inequalities for Differentiable Functions(Mdpi, 2022) Sial, Ifra Bashir; Patanarapeelert, Nichaphat; Ali, Muhammad Aamir; Budak, Hüseyin; Sitthiwirattham, ThaninIn this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski-Mercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of the Ostrowski inequalities established inside the literature. There are also some applications to the special means of real numbers given.Öğe On some Newton’s type inequalities for differentiable convex functions via Riemann-Liouville fractional integrals(University of Nis, 2023) Ali, Muhammad Aamir; Budak, Hüseyin; Fe?kan, M.; Patanarapeelert, N.; Sitthiwirattham, ThaninIn this paper, we establish a new integral identity involving Riemann-Liouville fractional integrals and differentiable functions. Then, we use the newly established identity and prove several Newton’s type inequalities for differentiable convex functions and functions of bounded variation. Moreover, we give a mathematical example and graphical analysis of newly established inequalities to show their validity. © 2023, University of Nis. All rights reserved.Öğe Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes(Amer Inst Mathematical Sciences-Aims, 2021) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, Hüseyin; Chasreechai, SaowaluckIn this paper, we introduce the notions of q-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as q, q(1), q(2) -> 1(-) in the newly obtained results.Öğe Riemann-Liouville Fractional Newton's Type Inequalities for Differentiable Convex Functions(Mdpi, 2022) Sitthiwirattham, Thanin; Nonlaopon, Kamsing; Ali, Muhammad Aamir; Budak, HüseyinIn 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.Öğe 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, ThaninIn 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.Öğe Some New Simpson's and Newton's Formulas Type Inequalities for Convex Functions in Quantum Calculus(Mdpi, 2021) Siricharuanun, Pimchana; Erden, Samet; Ali, Muhammad Aamir; Budak, Hüseyin; Chasreechai, Saowaluck; Sitthiwirattham, ThaninIn this paper, using the notions of q(kappa 2)-quantum integral and q(kappa 2)-quantum derivative, we present some new identities that enable us to obtain new quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors.Öğe 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, IbrahimIn 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.
