Yazar "Abbas, Mujahid" seçeneğine göre listele

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    Fractional integral inequalities for generalized convexity
    (Tbilisi Centre Math Sci, 2020) Kashuri, Artion; Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hiiseyin; Sarikaya, 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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    Generalization of quantum calculus and corresponding Hermite-Hadamard inequalities
    (Springer Basel Ag, 2024) Akbar, Saira Bano; Abbas, Mujahid; Budak, Hueseyin
    The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called (phi-h) integrals and (phi-h) derivatives, respectively. Then we investigate some implicit integral inequalities for (phi-h) integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite-Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and & hstrok;-convex functions defined on the non-negative part of the real line.
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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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    A new generalization of some quantum integral inequalities for quantum differentiable convex functions
    (Springer, 2021) Li, Yi-Xia; Ali, Muhammad Aamir; Budak, Huseyin; Abbas, Mujahid; Chu, Yu-Ming
    In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite-Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite-Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint-trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.
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    New quantum boundaries for quantum Simpson's and quantum Newton's type inequalities for preinvex functions
    (Springer, 2021) Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Huseyin; Agarwal, Praveen; Murtaza, Ghulam; Chu, Yu-Ming
    In this research, we derive two generalized integral identities involving the q kappa 2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson's and quantum Newton's inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson's and Newton's type inequalities by considering the limit q -> 1- in the key results of this paper.
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    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, Huseyin; Abbas, Mujahid; Muhammad, Faheem; Sitthiwirattham, Thanin
    In 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.
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    Quantum Hermite-Hadamard-type inequalities for functions with convex absolute values of second qb-derivatives
    (Springer, 2021) Ali, Muhammad Aamir; Budak, Huseyin; Abbas, Mujahid; Chu, Yu-Ming
    In this paper, we obtain Hermite-Hadamard-type inequalities of convex functions by applying the notion of qb-integral. We prove some new inequalities related with right-hand sides of qb-Hermite-Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard inequalities.