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    Fractional Ostrowski Type Inequalities for Interval Valued Functions
    (Univ Nis, Fac Sci Math, 2022) Budak, Hüseyin; Kashuri, Artion; Butt, Saad Ihsan
    In this paper, we establish some generalization of Ostrowski type inequalities for interval valued functions by using the definitions of the gH-derivatives. At the end, a briefly conclusion is given as well.
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    New Estimates for Hermite-Hadamard Inequality in Quantum Calculus via (alpha, m) Convexity
    (Mdpi, 2022) Xu, Peng; Butt, Saad Ihsan; Ul Ain, Qurat; Budak, Hüseyin
    This study provokes the existence of quantum Hermite-Hadamard inequalities under the concept of q-integral. We analyse and illustrate a new identity for the differentiable function mappings whose second derivatives in absolute value are (alpha, m) convex. Some basic inequalities such as Holder's and Power mean have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. We make links between our findings and a number of well-known discoveries in the literature. The conclusion in this study unify and generalise previous findings on Hermite-Hadamard inequalities.
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    New Quantum Mercer Estimates of Simpson-Newton-like Inequalities via Convexity
    (Mdpi, 2022) Butt, Saad Ihsan; Budak, Hüseyin; Nonlaopon, Kamsing
    Recently, developments and extensions of quadrature inequalities in quantum calculus have been extensively studied. As a result, several quantum extensions of Simpson's and Newton's estimates are examined in order to explore different directions in quantum studies. The main motivation of this article is the development of variants of Simpson-Newton-like inequalities by employing Mercer's convexity in the context of quantum calculus. The results also give new quantum bounds for Simpson-Newton-like inequalities through Holder's inequality and the power mean inequality by employing the Mercer scheme. The validity of our main results is justified by providing examples with graphical representations thereof. The obtained results recapture the discoveries of numerous authors in quantum and classical calculus. Hence, the results of these inequalities lead us to the development of new perspectives and extensions of prior results.
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    New quantum variants of Simpson-newton type inequalities via (?, m)-convexity
    (Kangwon-Kyungki Mathematical Soc, 2023) Butt, Saad Ihsan; Ul Ain, Qurat; Budak, Hüseyin
    . In this article, we will utilize (a, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using qe1-integral and qe1derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Holder's and Power mean, have been used to acquire new bounds.
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    New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen-Mercer Inequality
    (Mdpi, 2023) Butt, Saad Ihsan; Umar, Muhammad; Budak, Hüseyin
    The objective of this study is to identify novel quantum midpoint-type inequalities for twice q-differentiable functions by utilizing Mercer's approach. We introduce a new auxiliary variant of the quantum Mercer midpoint-type identity related to twice q-differentiable functions. By applying the theory of convex functions to this identity, we introduce new bounds using well-known inequalities, such as Holder's inequality and power-mean inequality. We provide explicit examples along with graphical demonstrations. The findings of this study explain previous studies on midpoint-type inequalities. Analytic inequalities of this type, as well as related strategies, have applications in various fields where symmetry plays an important role.
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    New Variants of Quantum Midpoint-Type Inequalities
    (Mdpi, 2022) Butt, Saad Ihsan; Budak, Hüseyin; Nonlaopon, Kamsing
    Recently, there has been a strong push toward creating and expanding quadrature inequalities in quantum calculus. In order to investigate various avenues for quantum inquiry, a number of quantum extensions of midpoint estimations are studied. The goal of this research article is to discover novel quantum midpoint-type inequalities that are twice q(xi 2)-differentiable for (alpha,m)-convex functions. Firstly, we obtain novel identity for q(xi 2)-integral by employing quantum calculus tools. Then by using the auxiliary identity, we formulate new bounds by taking into account the known quantum Holder and Power mean inequalities. An example is provided with a graphical representation to show the validity of obtaining results. The outcomes of this study clarify and expand earlier research on midpoint-type inequalities. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.
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    Novel q-Differentiable Inequalities
    (Mdpi, 2023) Zuo, Xuewu; Butt, Saad Ihsan; Umar, Muhammad; Budak, Hüseyin; Ali, Muhammad Aamir; Dolgy, Dmitry V.
    The striking goal of this study is to introduce a q-identity for a parameterized integral operator via differentiable function. First, we discover the parameterized lemma for the q-integral. After that, we provide several q-differentiable inequalities. By taking suitable choices, some interesting results are obtained. With all of these, we displayed the findings from the traditional analysis utilizing q & RARR;1-.