Yazar "Ali, Muhammad Aamir" seçeneğine göre listele

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    Extensions of Hermite-Hadamard inequalities for harmonically convex functions via generalized fractional integrals
    (Springer, 2021) You, Xue-Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Agarwal, Praveen; Chu, Yu-Ming
    In the paper, the authors establish some new Hermite-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite-Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.
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    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, Michal
    In 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.
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    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, Thanin
    We 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.
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    Fractional Hermite-Hadamard Type Inequalities for Subadditive Functions
    (Univ Nis, Fac Sci Math, 2022) Ali, Muhammad Aamir; Sarıkaya, Mehmet Zeki; Budak, Hüseyin
    In this paper, we establish different variants of fractional Hermite-Hadamard inequalities for subadditive functions via Riemann-Liouville fractional integrals. Moreover, we offer some fractional integral inequalities for the product of two subadditive functions via Riemann-Liouville fractional integrals. It is also shown that the inequalities offered in this research are the generalization of the already given inequalities for convex functions and subadditive functions.
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    Fractional integral inequalities for generalized convexity
    (Tbilisi Centre Math Sci, 2020) Kashuri, Artion; Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hiiseyin; Sarıkaya, Mehmet Zeki
    In this paper, we define a new class of functions called generalized phi-convex function. Several variants of Hermite-Hadamard type fractional integral inequalities are presented. This ideas and techniques used in this paper may open new avenues of research and motivate the reader to explore the application of generalized phi-convex functions in various branches of pure and applied sciences.
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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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    Fractional trapezoid and newton type inequalities for differentiable s-convex functions
    (Honam Mathematical Soc, 2023) Hezenci, Fatih; Budak, Hüseyin; Ali, Muhammad Aamir
    In the present paper, we prove that our main inequality re-duces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.
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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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    Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions
    (De Gruyter Poland Sp Z O O, 2022) Vivas-Cortez, Miguel J. J.; Kara, Hasan; Budak, Hüseyin; Ali, Muhammad Aamir; Chasreechai, Saowaluck
    In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.
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    Generalized fractional integral inequalities for product of two convex functions
    (Forum Editrice Univ Udinese, 2021) Ali, Muhammad Aamir; Budak, Hüseyin; Sial, Ifra Bashir
    The aim of this paper is to generalize the results proved in [4] using generalized fractional integral. Some special cases are deduced from main results. Applying the techniques of our results, new results may be obtained during a similar manner for various operators.
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    Generalized fractional integral inequalities of Hermite-Hadamard type for harmonically convex functions
    (Springeropen, 2020) Zhao, Dafang; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin
    In this paper, we establish inequalities of Hermite-Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (Iscan in Hacet. J. Math. Stat. 43(6):935-942, 2014 and Iscan and Wu in Appl. Math. Comput. 238:237-244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite-Hadamard type.
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    GENERALIZED QUANTUM MONTGOMERY IDENTITY AND OSTROWSKI TYPE INEQUALITIES FOR PREINVEX FUNCTIONS
    (Inst Applied Mathematics, 2022) Kalsoom, Humaira; Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hüseyin; MURTAZA, GHULAM
    In this research, we give a generalized version of the quantum Montgomery identity using the quantum integral. We establish some new inequalities of Ostrowski type by means of newly derived identity. Moreover, we consider the special cases of the newly obtained results and prove several new and known Ostrowski and midpoint 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, Hüseyin; 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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    HERMITE-HADAMARD INTEGRAL INEQUALITIES FOR LOG-CONVEX INTERVAL-VALUED FUNCTIONS ON CO-ORDINATES
    (Turkic World Mathematical Soc, 2022) Ali, Muhammad Aamir; Murtaza, G.; Budak, Hüseyin
    In this paper, we give the notion of interval-valued log-convex functions on the co-ordinates on the rectangle from the plane. We establish Hermite-Hadamard and related inequalities for these classes of functions. Our results are refinements of several existing results in the field of Hermite-Hadamard inequalities. Some examples are also given to justify our new results.
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    HERMITE-HADAMARD TYPE INEQUALITIES AND RELATED INEQUALITIES FOR SUBADDITIVE FUNCTIONS
    (Univ Miskolc Inst Math, 2021) Sarıkaya, Mehmet Zeki; Ali, Muhammad Aamir
    In this paper, we establish Hermite-Hadamard inequalities for subadditive functions, and we give some related inequalities according to Hermite-Hadamard inequalities, which generalized the previously published results.
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    Hermite-Hadamard type inequalities for F-convex functions involving generalized fractional integrals
    (Babes-Bolyai University, 2022) Budak, Hüseyin; Ali, Muhammad Aamir; Kashuri, Artion
    In this paper, we firstly summarize some properties of the family ? and F-convex functions which are defined by B. Samet. Utilizing generalized fractional integrals new Hermite-Hadamard type inequalities for F-convex functions have been provided. Some results given earlier works are also as special cases of our results. © 2022, Studia Universitatis Babes-Bolyai Mathematica. All rights reserved.
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    Hermite-Hadamard Type Inequalities For The Interval-Valued Harmonically h-Convex Functions Via Fractional Integrals
    (Tsing Hua Univ, Dept Mathematics, 2021) Budak, Hüseyin; Bilisik, Condon Can; Kashuri, Artion; Ali, Muhammad Aamir
    In this paper, we first present a new definition of convex interval-valued functions which is called as interval-valued harmonically h-convex functions. Then, we establish some new Hermite-Hadamard type inequalities for interval-valued harmonically h-convex functions by using fractional integrals. We also discussed some special cases of our main results. Finally, a briefly conclusion is given.
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    Hermite-Hadamard type inequalities for the interval-valued harmonically h-convex functions via fractional integrals
    (Tsing Hua University, 2021) Budak, Hüseyin; Bilişik, Özge Nalan; Kashuri, Artion; Ali, Muhammad Aamir
    In this paper, we first present a new definition of convex interval-valued functions which is called as interval-valued harmonically h-convex functions. Then, we establish some new Hermite-Hadamard type inequalities for interval-valued harmonically h-convex functions by using fractional integrals. We also discussed some special cases of our main results. Finally, a briefly conclusion is given. © 2021, Tsing Hua University. All rights reserved.
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    Hermite-Hadamard-Mercer type inclusions for interval-valued functions via Riemann-Liouville fractional integrals
    (Scientific Technical Research Council Turkey-Tubitak, 2022) Kara, Hasan; Ali, Muhammad Aamir; Budak, Hüseyin
    In this research, we first establish some inclusions of fractional Hermite???Hadamard???Mercer type for interval -valued functions. Moreover, by special cases of our main results, we show that our main results reduce several inclusions obtained in the earlier works.
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    Hermite-Hadamard-Mercer-Type Inequalities for Harmonically Convex Mappings
    (Mdpi, 2021) You, Xuexiao; Ali, Muhammad Aamir; Budak, Hüseyin; Reunsumrit, Jiraporn; Sitthiwirattham, Thanin
    In 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.