نامساوی هرمیت - هادامارد برای توابع $(\alpha,m)$- محدب

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی، واحد زنجان، دانشگاه آزاد اسلامی، زنجان، ایران

چکیده

در این مقاله بعد از معرفی خاصیت m −محدب توسط تادر به عنوان یک خاصیت میانی بین تحدب کلی و

ستاره شکل، نامساوی انتگرال هرمیت‐هادامارد را برای تابع (m, α) −محدب در قالب جدید بیان و ثابت می کنیم.

نتایج قبلی در مورد نامساوی هرمیت ‐ هادامارد برای توابع m −محدب بخشی از نتایج قضایای مایند. مثال هایی در

خصوص توابع (m, α) −محدب و m −محدب نیز در مقاله گنجانده شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

HERMITE-HADAMARD INTEGRAL INEQUALITY FOR $(\alpha,m)$-CONVEX FUNCTIONS

نویسنده [English]

  • Mehdi Asadi
Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran
چکیده [English]

In this paper, after introducing the $m$-convexity by Toader, as an intermediate among the general convexity and star shaped property, we bring Hermite-Hadamard integral inequality on $(\alpha,m)$-convex function in the new form. Previous results about the Hermite-Hadamard inequality for $m$-convex functions are part of the results of our theorems. Illustrated examples of $(\alpha,m)$-convex and $m$-convex functions are also included in the article.

کلیدواژه‌ها [English]

  • Hermite-Hadamard integral inequality
  • m
  • -convex function
  • convex functions
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