Yazar "Gulshan, Ghazala" seçeneğine göre listele

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    Generalization of the bisection method and its applications in nonlinear equations
    (Springer, 2023) Gulshan, Ghazala; Budak, Hüseyin; Hussain, Rashida; Sadiq, Asad
    The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for each q ? (0,1) is also determined. Some physical problems in engineering are resolved using the QBM technique for various values of the quantum parameter q up to three iterations to examine the validity of the method. Furthermore, it is proven that QBM is always convergent and that for each interval there exists q ? (0,1) for which the first approximation of root coincides with the precise solution of the problem.
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    A NEW GENERALIZATION OF q-HERMITE-HADAMARD TYPE INTEGRAL INEQUALITIES FOR p, (p-s) AND MODIFIED (p-s)-CONVEX FUNCTIONS
    (Element D.O.O., 2022) Gulshan, Ghazala; Hussain, R.; Budak, Hüseyin
    In this study, we develop three new quantum Hermite-Hadamard inequalities for the class of p, (p-s) and modified type ( p-s) -convex functions by utilizing left and right quantum integral. As special cases of these inequalities, we get known and new Hermite-Hadamard type inequality for modified type (p-s) -convex functions. The ideas and techniques of this article may be the starting point for further research in this field. © 2023 Rockefeller University Press. All rights reserved.
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    New Quantum Hermite-Hadamard-Type Inequalities for p-Convex Functions Involving Recently Defined Quantum Integrals
    (Springer, 2024) Gulshan, Ghazala; Budak, Hueseyin; Hussain, Rashida; Ali, Muhammad Aamir
    We develop new Hermite-Hadamard-type integral inequalities for p-convex functions in the context of q-calculus by using the concept of recently defined T-q-integrals. Then the obtained Hermite-Hadamard inequality for p-convex functions is used to get a new Hermite-Hadamard inequality for coordinated p-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the proposed ideas and techniques may stimulate further research in this field.
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    On generalizations of post quantum midpoint and trapezoid type inequalities for (a, m)-convex functions
    (Univ Nis, Fac Sci Math, 2023) Gulshan, Ghazala; Budak, Hüseyin; Hussain, Rashida; Sadiq, Asad
    The aim of current study is to establish two crucial (p, q)b-integral identities for midpoint and trapezoid type inequalities. Utilizing these identities, we developed some new variant of midpoint and trapezoid type integral inequalities of differential (alpha, m)-convex functions using right post quantum integral approach. Moreover, we have presented the application of derived results related to special means of positive real numbers.
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    On some generalized Simpson type inequalities for (a,m)-coordinated convex functions in context of q1q2-calculus
    (Walter De Gruyter Gmbh, 2023) Gulshan, Ghazala; Ali, Muhammad Aamir; Hussain, Rashida; Sadiq, Asad; Budak, Hüseyin
    In the current investigation, we offer the generalized version of q(1)q(2)-Simpson's type inequalities via (a , m)-coordinated convex functions. To validate their generalized behavior, we demonstrate the link between our outcomes and the already derived ones. Moreover, we provide some application to special means of pos-itive real numbers to support our findings. The principal outcomes raised in this investigation are extensions and generalizations of the comparable results in the history on Simpson's inequalities for coordinated convex functions.
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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.