Browsing by Author "Kamsing Nonlaopon"

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    On some SimpsonÕs and NewtonÕs type of inequalities in multiplicative calculus with applications
    (American Institute of Mathematical Sciences, 2023) Saowaluck Chasreechai; Muhammad Aamir Ali; Surapol Naowarat; Thanin Sitthiwirattham; Kamsing Nonlaopon; K. Nonlaopon; Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand; email: nkamsi@kku.ac.th
    In this paper, we establish an integral equality involving a multiplicative differentiable function for the multiplicative integral. Then, we use the newly established equality to prove some new SimpsonÕs and NewtonÕs inequalities for multiplicative differentiable functions. Finally, we give some mathematical examples to show the validation of newly established inequalities. © 2023 the Author(s), licensee AIMS Press.
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    RiemannÐLiouville Fractional NewtonÕs Type Inequalities for Differentiable Convex Functions
    (MDPI, 2022) Thanin Sitthiwirattham; Kamsing Nonlaopon; Muhammad Aamir Ali; HŸseyin Budak; K. Nonlaopon; Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand; email: nkamsi@kku.ac.th
    In this paper, we prove some new NewtonÕs type inequalities for differentiable convex functions through the well-known RiemannÐLiouville fractional integrals. Moreover, we prove some inequalities of RiemannÐLiouville fractional NewtonÕs type for functions of bounded variation. It is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. Finally, we give some examples with graphs and show the validity of newly established inequalities. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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    Some New Generalized Fractional Newton's Type Inequalities for Convex Functions
    (Hindawi Limited, 2022) Jarunee Soontharanon; Muhammad Aamir Ali; HŸseyin Budak; Pinar Kšsem; Kamsing Nonlaopon; Thanin Sitthiwirattham; K. Nonlaopon; Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand; email: nkamsi@kku.ac.th
    In this paper, we establish some new Newton's type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k-fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature. © 2022 Jarunee Soontharanon et al.