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Characterizations of Higher Order Strongly Generalized Convex Functions

In: Nonlinear Analysis, Differential Equations, and Applications

Author

Listed:
  • Muhammad Aslam Noor

    (COMSATS University Islamabad)

  • Khalida Inayat Noor

    (COMSATS University Islamabad)

  • Michael Th. Rassias

    (University of Zurich
    Moscow Institute of Physics and Technology
    Program in Interdisciplinary Studies)

Abstract

In this paper, we define and consider some new concepts of the higher order strongly generalized convex functions with respect to two arbitrary functions. Some properties of the higher order strongly generalized convex functions are investigated under suitable conditions. It is shown that the operator parallelogram laws for the characterization of uniformly Banach spaces can be obtained as a novel applications of higher order strongly affine functions. It is shown that the optimality conditions of the higher order strongly generalized convex functions are characterized by a new class of variational inequalities. Some special cases also discussed. Results obtained in this paper can be viewed as significant refinement and improvement of previously known results.

Suggested Citation

  • Muhammad Aslam Noor & Khalida Inayat Noor & Michael Th. Rassias, 2021. "Characterizations of Higher Order Strongly Generalized Convex Functions," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 341-364, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-72563-1_15
    DOI: 10.1007/978-3-030-72563-1_15
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    Cited by:

    1. Muhammad Bilal Khan & Gustavo Santos-García & Hatim Ghazi Zaini & Savin Treanță & Mohamed S. Soliman, 2022. "Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus," Mathematics, MDPI, vol. 10(4), pages 1-26, February.

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