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Some results on Simpson type conformable fractional inequalities

Zeynep Şanlı

Abstract

In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to some special means of real numbers and two special functions, modified Bessel function and q-digamma function, respectively.

Some results on Simpson type conformable fractional inequalities

Abstract

In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to some special means of real numbers and two special functions, modified Bessel function and q-digamma function, respectively.

Paper Structure

This paper contains 10 sections, 18 theorems, 76 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results
  4. Estimation Results
  5. Applications
  6. Special Means
  7. Inequalities for some special functions.
  8. Modified Bessel function.
  9. $q-$digamma function
  10. Conclusion

Key Result

Theorem 1

Let $\psi:\left[ \gamma,\delta\right] \rightarrow\mathbb{R}$ be a four times continuously differentiable mapping on $\left( \gamma,\delta\right)$ and $\left\Vert \psi^{\left( 4\right) }\right\Vert _{\infty}=\sup\left\vert \psi^{\left( 4\right) }\left( \varepsilon\right) \right\vert <\infty.$

Theorems & Definitions (46)

  • Theorem 1
  • Lemma 1
  • Theorem 2
  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 2
  • proof
  • Remark 1
  • Remark 2
  • ...and 36 more