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Generalized Hermite–Hadamard type inequalities for generalized F-convex function via local fractional integrals

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  • Razzaq, Arslan
  • Rasheed, Tahir
  • Shaokat, Shahid

Abstract

In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets Rς (0<ς≤1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite–Hadamard type inequalities in the fractals sense. In this work, we present some new results by employing local fractional calculus for twice differentiable functions along with some new definitions. For the development of these new integral inequalities, we will use generalized Hölder-integral inequality and power mean integral inequality by using local fractional calculus. Moreover, we give some new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works.

Suggested Citation

  • Razzaq, Arslan & Rasheed, Tahir & Shaokat, Shahid, 2023. "Generalized Hermite–Hadamard type inequalities for generalized F-convex function via local fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000735
    DOI: 10.1016/j.chaos.2023.113172
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    References listed on IDEAS

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    1. Erden, Samet & Sarikaya, Mehmet Zeki, 2016. "Generalized Pompeiu type inequalities for local fractional integrals and its applications," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 282-291.
    2. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    3. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Yang Zhao & De-Fu Cheng & Xiao-Jun Yang, 2013. "Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-5, September.
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