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On Strongly Generalized Preinvex Fuzzy Mappings

Author

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  • Peide Liu
  • Muhammad Bilal Khan
  • Muhammad Aslam Noor
  • Khalida Inayat Noor
  • Kaleem R. Kazmi

Abstract

In this article, we introduce a new notion of generalized convex fuzzy mapping known as strongly generalized preinvex fuzzy mapping on the invex set. Firstly, we have investigated some properties of strongly generalized preinvex fuzzy mapping. In particular, we establish the equivalence among the strongly generalized preinvex fuzzy mapping, strongly generalized invex fuzzy mapping, and strongly generalized monotonicity. We also prove that the optimality conditions for the sum of G-differentiable preinvex fuzzy mappings and non-G-differentiable strongly generalized preinvex fuzzy mappings can be characterized by strongly generalized fuzzy mixed variational-like inequalities, which can be viewed as a novel and innovative application. Several special cases are discussed. Results obtained in this paper can be viewed as improvement and refinement of previously known results.

Suggested Citation

  • Peide Liu & Muhammad Bilal Khan & Muhammad Aslam Noor & Khalida Inayat Noor & Kaleem R. Kazmi, 2021. "On Strongly Generalized Preinvex Fuzzy Mappings," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, April.
    • Handle: RePEc:hin:jjmath:6657602
    DOI: 10.1155/2021/6657602
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    Cited by:

    1. Abdullah Ali H. Ahmadini & Waqar Afzal & Mujahid Abbas & Elkhateeb S. Aly, 2024. "Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems," Mathematics, MDPI, vol. 12(3), pages 1-28, January.

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