Browsing by Publisher "American Institute of Mathematical Sciences"

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    Perturbed trapezoid inequalities for n th order differentiable convex functions and their applications
    (American Institute of Mathematical Sciences, 2020) Demir D.D.; Şanal G.
    In this study, we introduce a new general identity for n th order differentiable functions. Also, we establish some new inequalities regarding general perturbed trapezoid inequality for the functions whose the absolute values of n th derivatives are convex. Finally, some applications for special means are provided. © 2020 the Author(s), licensee AIMS Press.
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    New approximate solutions to the nonlinear Klein-Gordon equations using perturbation iteration techniques
    (American Institute of Mathematical Sciences, 2020) Bildik N.; Deniz S.
    In this study, we present the new approximate solutions of the nonlinear Klein-Gordon equations via perturbation iteration technique and newly developed optimal perturbation iteration method. Some specific examples are given and obtained solutions are compared with other methods and analytical results to confirm the good accuracy of the proposed methods.We also discuss the convergence of the optimal perturbation iteration method for partial differential equations. The results reveal that perturbation iteration techniques,unlike many other techniques in literature, converge rapidly to exact solutions of the given problems at lower order of approximations. © 2020 American Institute of Mathematical Sciences. All rights reserved.