Yazar "Kalsoom, Humaira" seçeneğine göre listele

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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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    On new generalized quantum integrals and related Hermite-Hadamard inequalities
    (Springer, 2021) Kara, Hasan; Budak, Hüseyin; Alp, Necmettin; Kalsoom, Humaira; Sarıkaya, Mehmet Zeki
    In this article, we introduce a new concept of quantum integrals which is called T-kappa 2(q)-integral. Then we prove several properties of this concept of quantum integrals. Moreover, we present several Hermite-Hadamard type inequalities for T-kappa 2(q)-integral by utilizing differentiable convex functions. The results presented in this article are unification and generalization of the comparable results in the literature.
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    q-Hermite-Hadamard Inequalities for Generalized Exponentially (s, m; eta)-Preinvex Functions
    (Hindawi Ltd, 2021) Wang, Hua; Kalsoom, Humaira; Budak, Hüseyin; Idrees, Muhammad
    In this article, we introduce a new extension of classical convexity which is called generalized exponentially (s, m; eta)-preinvex functions. Also, it is seen that the new definition of generalized exponentially (s, m; eta)-preinvex functions describes different new classes as special cases. To prove our main results, we derive a new (m kappa 2)q-integral identity for the twice (m kappa 2)q-differentiable function. By using this identity, we show essential new results for Hermite-Hadamard-type inequalities for the (m kappa 2)q-integral by utilizing differentiable exponentially (s, m; eta)-preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.
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    Quantum Inequalities of Hermite-Hadamard Type for r-Convex Functions
    (Hindawi Ltd, 2021) You, Xuexiao; Kara, Hasan; Budak, Hüseyin; Kalsoom, Humaira
    In this present study, we first establish Hermite-Hadamard type inequalities for r-convex functions via (q)(k2)-definite integrals. Then, we prove some quantum inequalities of Hermite-Hadamard type for product of two r-convex functions. Finally, by using these established inequalities and the results given by (Brahim et al. 2015), we prove several quantum Hermite-Hadamard type inequalities for coordinated r-convex functions and for the product of two coordinated r-convex functions.
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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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    Some new parameterized inequalities for co-ordinated convex functions involving generalized fractional integrals
    (De Gruyter Poland Sp Z O O, 2021) Kalsoom, Humaira; Budak, Hüseyin; Kara, Hasan; Ali, Muhammad Aamir
    In this study, we first obtain a new identity for generalized fractional integrals which contains some parameters. Then by this equality, we establish some new parameterized inequalities for co-ordinated convex functions involving generalized fractional integrals. Moreover, we show that the results proved in the main section reduce to several Simpson-, trapezoid-and midpoint-type inequalities for various values of parameters.