IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v168y2023ics0960077923000735.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923000735
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113172?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    2. Huynh Ngai & Nguyen Huu Tron & Nguyen Vu & Michel Théra, 2022. "Variational Analysis of Paraconvex Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 180-218, June.
    3. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    4. T. R. Gulati & I. Ahmad & D. Agarwal, 2007. "Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 411-427, December.
    5. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    6. S. Nobakhtian, 2006. "Sufficiency in Nonsmooth Multiobjective Programming Involving Generalized (Fρ)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 361-367, August.
    7. Sorger, Gerhard, 1995. "On the sensitivity of optimal growth paths," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 353-369.
    8. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
    9. Sedi Bartz & Minh N. Dao & Hung M. Phan, 2022. "Conical averagedness and convergence analysis of fixed point algorithms," Journal of Global Optimization, Springer, vol. 82(2), pages 351-373, February.
    10. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    11. Hugo Leiva & Nelson Merentes & Kazimierz Nikodem & José Sánchez, 2013. "Strongly convex set-valued maps," Journal of Global Optimization, Springer, vol. 57(3), pages 695-705, November.
    12. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    13. Venditti Alain, 2019. "Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-14, September.
    14. Anurag Jayswal & Vivek Singh & Krishna Kummari, 2017. "Duality for nondifferentiable minimax fractional programming problem involving higher order $$(\varvec{C},\varvec{\alpha}, \varvec{\rho}, \varvec{d})$$ ( C , α , ρ , d ) -convexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 598-617, September.
    15. Albert Ferrer & Adil Bagirov & Gleb Beliakov, 2015. "Solving DC programs using the cutting angle method," Journal of Global Optimization, Springer, vol. 61(1), pages 71-89, January.
    16. Francisco Facchinei & Jong-Shi Pang & Gesualdo Scutari, 2014. "Non-cooperative games with minmax objectives," Computational Optimization and Applications, Springer, vol. 59(1), pages 85-112, October.
    17. Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.
    18. Giancarlo Bigi & Mauro Passacantando, 2017. "Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 63-79, November.
    19. David Barilla & Giuseppe Caristi & Nader Kanzi, 2022. "Optimality and duality in nonsmooth semi-infinite optimization, using a weak constraint qualification," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 503-519, December.
    20. F. Lara, 2022. "On Strongly Quasiconvex Functions: Existence Results and Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 891-911, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000735. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.