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Generalization of Hermite-Hadamard-Mercer]{Generalization of Hermite-Hadamard-Mercer and Trapezoid Formula Type Inequalities Involving Beta Function
  • Muhammad Aamir Ali,
  • Zhiyue Zhang
Muhammad Aamir Ali
Nanjing Normal University School of Mathematical Sciences
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Zhiyue Zhang
Nanjing Normal University

Corresponding Author:[email protected]

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In this work, we prove a generalized version of Hermite-Hadamard-Mercer type inequalities using the Beta function. Moreover, we prove some new trapezoidal type inequalities involving Beta functions for differentiable convex functions. The main advantage of these inequalities is that these can be converted into similar classical integral inequalities, Riemann-Liouville fractional integral inequalities and $k$-Riemann-Liouville fractional integral inequalities. Finally, we give applications to special means of real numbers for newly established inequalities.