Browsing by Author "FA20-RMT-038"

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    Newton and Simpson Formula Type Inequalities Via Generalized Convexity in Quantum Calculus
    (Library Information Services, CUI Lahore, 2022) Qurat Ul Ain Tariq; FA20-RMT-038; Dr. Saad Ihsan Butt
    In this proposal, we will establish a novel form of Newton’s and Simpson’s inequalities in quantum calculus by using (a; m)-convexity. Newly obtained inequalities may be con- verted into Simpson and Newton inequalities in quantum for generalized convex functions by using q1-integral. Thus, these developments allow us to develop new bounds for quantum integral inequalities. In this research work we will present some new results by employing quantum calculus for differentiable functions and we will also give some new applications along with some new definitions. For the development of these new quantum integral inequalities, we will use Holder and Power mean integral inequalities by using quantum calculus. The discoveries of numerous authors in quantum and classical calculus were broadened and expanded in this paper. Hence, these new results will lead us to generalization of prior results.
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    Newton and Simpson Formula Type Inequalities Via Generalized Convexity in Quantum Calculus
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Qurat UL Ain Tariq; FA20-RMT-038; LHR TP 7939
    This study establishes Newton- and Simpson-type integral inequalities within the framework of generalized convexity in quantum calculus. By extending classical convexity concepts to the quantum calculus setting, new bounds are derived for differentiable functions defined on quantum time scales. The work develops refined integral inequalities using generalized convex functions, providing sharper estimates than their classical counterparts. Newton and Simpson-type formulas are adapted to incorporate q-calculus operators, and the resulting inequalities are analyzed for accuracy and convergence behavior. Applications of these results are discussed in numerical integration and approximation theory. The findings demonstrate that generalized convexity in quantum calculus offers powerful tools for improving classical numerical inequality estimates.