Yazar "Awan, Muhammad Uzair" 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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    Exploring Quantum Simpson-Type Inequalities for Convex Functions: A Novel Investigation
    (Mdpi, 2023) Iftikhar, Sabah; Awan, Muhammad Uzair; Budak, Hueseyin
    This study seeks to derive novel quantum variations of Simpson's inequality by primarily utilizing the convexity characteristics of functions. Additionally, the study examines the credibility of the obtained results through the presentation of relevant numerical examples and graphs.
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    Generalized AB-Fractional Operator Inclusions of Hermite-Hadamard's Type via Fractional Integration
    (Mdpi, 2023) Bin-Mohsin, Bandar; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Khan, Awais Gul; Budak, Huseyin; Mihai, Marcela V.; Noor, Muhammad Aslam
    The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function E-mu,alpha,l(gamma,delta, k,c) (tau; p) as a kernel in the interval domain. Additionally, a new form of Atangana-Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in E-mu,alpha,l(gamma,delta, k,c)(tau; p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.
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    Inclusions Involving Interval-Valued Harmonically Co-Ordinated Convex Functions and Raina's Fractional Double Integrals
    (Hindawi Ltd, 2022) Bin Mohsin, Bandar; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Budak, Hüseyin; Khan, Awais Gul; Noor, Muhammad Aslam
    The aim of this article is to obtain some new integral inclusions essentially using the interval-valued harmonically co-ordinated convex functions and kappa-Raina's fractional double integrals. To show the validity of our theoretical results, we also give some numerical examples.
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    Jensen-Mercer Type Inequalities in the Setting of Fractional Calculus with Applications
    (Mdpi, 2022) Bin Mohsin, Bandar; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Mihai, Marcela, V; Budak, Hüseyin; Khan, Awais Gul; Noor, Muhammad Aslam
    The main objective of this paper is to establish some new variants of the Jensen-Mercer inequality via harmonically strongly convex function. We also propose some new fractional analogues of Hermite-Hadamard-Jensen-Mercer-like inequalities using AB fractional integrals. In order to obtain some of our main results, we also derive new fractional integral identities. To demonstrate the significance of our main results, we present some interesting applications to special means and to error bounds as well.
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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 some classical integral inequalities in the setting of new post quantum integrals
    (Amer Inst Mathematical Sciences-Aims, 2022) Bin Mohsin, Bandar; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Talib, Sadia; Budak, Hüseyin; Noor, Muhammad Aslam; Noor, Khalida Inayat
    In this article, we introduce the notion of aT over bar p,q-integrals. Using the definition of aT over bar p,q-integrals, we derive some new post quantum analogues of some classical results of Young's inequality, Ho center dot lder's inequality, Minkowski's inequality, Ostrowski's inequality and Hermite-Hadamard's inequality.
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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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    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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    Quantum Integral Inequalities in the Setting of Majorization Theory and Applications
    (Mdpi, 2022) Bin Mohsin, Bandar; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Budak, Hüseyin; Kara, Hasan; Noor, Muhammad Aslam
    In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over PO known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite-Hadamard type inequalities using the Jensen-Mercer inequality in the frame of q-calculus and majorized l-tuples. Firstly we derive q-Hermite-Hadamard-Jensen-Mercer (H.H.J.M) type inequalities with the help of Mercer's inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q-differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q-identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper.
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    Some q-Fractional Estimates of Trapezoid like Inequalities Involving Raina's Function
    (Mdpi, 2022) Nonlaopon, Kamsing; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Budak, Hüseyin; Noor, Muhammad Aslam
    In this paper, we derive two new identities involving q-Riemann-Liouville fractional integrals. Using these identities, as auxiliary results, we derive some new q-fractional estimates of trapezoidal-like inequalities, essentially using the class of generalized exponential convex functions.
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    A study of new quantum Montgomery identities and general Ostrowski like inequalities
    (Elsevier, 2024) Awan, Muhammad Uzair; Javed, Muhammad Zakria; Budak, Huseyin; Hamed, Y. S.; Ro, Jong-Suk
    The main objective of this paper is to analyze the Montgomery identities and Ostrowski like inequalities, within the framework of quantum calculus. The study utilizes w 3 q and w 4 q differentiable functions to establish two new Montgomery identities, which are essential for the development of our main results which are new quantum estimates of general Ostrowski type inequality. The study involves numerous techniques, including q -identities, H & ouml;lder-like inequalities, and the Jensen-Mercer inequality for convex mappings, to derive the main outcomes of the paper. Additionally, the study presents special cases, numerical validation, and graphical illustrations to support the main results.
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    Unified inequalities of the q-Trapezium-Jensen-Mercer type that incorporate majorization theory with applications
    (Amer Inst Mathematical Sciences-Aims, 2023) Bin-Mohsin, Bandar; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Budak, Huseyin; Khan, Awais Gul; Cesarano, Clemente; Noor, Muhammad Aslam
    The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of q-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the & sigma;1q and & sigma;2 q differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint q-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations.