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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


$q_e-$Fixed Point and $q_e-$Inverse Function Theorem $1D$

Discontinuity, Nonlinearity, and Complexity 15(3) (2026) 309--313 | DOI:10.5890/DNC.2026.09.001

J. A. Castillo, J. A. P. Moyado, T. Galeana, M.A. Herrera, Israel Herrera

Facultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero, Carlos E. Adame #54, Col. Garita, c.p. 39650, Acapulco, Gro., México

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Abstract

Using the definitions from [1] on the $q_e-$calculus we prove $q_e-$analogues of the Fixed Point Theorem and Inverse Function Theorem.

References

  1. [1]  Nápoles, J.E., Castillo, J.A., Guzmán, P.M., and Lugo, L.M. (2019), A new local fractional derivative of $q-$uniform type, Discontinuity, Nonlinearity, and Complexity, 8, 101-109.
  2. [2]  Spivak (2008), Calculus, Publish or Perish Inc., Texas, 4ed.
  3. [3]  Kac, V. and Cheung, P. (2001), Quantum Calculus, Springer Science & Business Media, New York.
  4. [4]  Bermudo, S., Kórus, P., and Nápoles Valdés, J.E.(2020), On q-Hermite-Hadamard inequalities for general convex functions, Acta Mathematica Hungarica, 162, 364-374. https://doi.org/10.1007/s10474-020-01025-6
  5. [5]  Castillo, J.A., Cruz, S., Nápoles, J.E., and Galeana, T. (2021), Some new results on $q$-calculus, Discontinuity, Nonlinearity, and Complexity, 4(12), 733-741.