• Honam Mathematical Journal
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• v.44 no.3
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• pp.325-338
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• 2022

In this paper, a new identity is given. On the basis of this identity, we establish some new estimates of Milne's quadrature rule, for functions whose first derivative is s-convex. We discuss the cases where the derivatives are bounded as well as Lipschitzian. Some illustrative applications are given.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.523-536
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• 2007

Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.3
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• pp.212-217
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• 2007

The Alienor method is a powerful tool for solving global optimization problems. It allows the transformation of a multi-variable problem into a new one that depends on a single variable. Any one-dimensional global optimization method can then be used to solve the transformed problem. Several one-dimensional global optimization methods coupled with the Alienor method have been suggested by mathematicians and it is shown that the suggested methods are successful for test functions. However, there are problems with these methods in engineering practice. In this paper, Lipschitzian optimization without using the Lipschitz constant is coupled with the Alienor method and applied to the test functions. Using test functions, it is shown that the suggested method can be successfully applied to global optimization problems.