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On the Generalized ( p , q )- ϕ -Calculus with Respect to Another Function

Author

Listed:
  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran)

  • Ivanka Stamova

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

Abstract

In the present paper, we generalized some of the operators defined in ( p , q ) -calculus with respect to another function. More precisely, the generalized ( p , q ) - ϕ -derivatives and ( p , q ) - ϕ -integrals were introduced with respect to the strictly increasing function ϕ with the help of different orders of the q -shifting, p -shifting, and ( q / p ) -shifting operators. Then, after proving some related properties, and as an application, we considered a generalized ( p , q ) - ϕ -difference problem and studied the existence property for its unique solutions with the help of the Banach contraction mapping principle.

Suggested Citation

  • Sina Etemad & Ivanka Stamova & Sotiris K. Ntouyas & Jessada Tariboon, 2024. "On the Generalized ( p , q )- ϕ -Calculus with Respect to Another Function," Mathematics, MDPI, vol. 12(20), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3290-:d:1502676
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    References listed on IDEAS

    as
    1. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "Some approximation results by (p, q)-analogue of Bernstein–Stancu operators," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 392-402.
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