Search Advanced

AIMS Mathematics

2023, Volume 8, Issue 4: 9385-9399. doi: 10.3934/math.2023472
Previous Article Next Article
Research article Special Issues

Generalized q-convex functions characterized by q-calculus

  • 1.
    Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
  • 2.
    Department of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif, AJK, Pakistan
  • 3.
    Department of Mathematics, College of Science, Al-Zulfi Majmaah University, Al-Majmaah 11952, Saudi Arabia
  • Received: 22 January 2022 Revised: 27 April 2022 Accepted: 24 May 2022 Published: 15 February 2023

  • MSC : 30C45, 30C10

  • The objective of the current examination is to present new sub-classes of q-convex and q-starlike functions inside E={z∈C:|z|<1}, by q-difference operator. We determined connections of these classes and acquired a few fundamental properties, for instance, inclusion relation, subordination properties and q-limits on real part.

    Citation: Aisha M. Alqahtani, Rashid Murtaza, Saba Akmal, Adnan, Ilyas Khan. Generalized q-convex functions characterized by q-calculus[J]. AIMS Mathematics, 2023, 8(4): 9385-9399. doi: 10.3934/math.2023472

    Related Papers:

    [1] Mapundi K. Banda, Michael Herty, Axel Klar . Gas flow in pipeline networks. Networks and Heterogeneous Media, 2006, 1(1): 41-56. doi: 10.3934/nhm.2006.1.41
    [2] Michael Herty . Modeling, simulation and optimization of gas networks with compressors. Networks and Heterogeneous Media, 2007, 2(1): 81-97. doi: 10.3934/nhm.2007.2.81
    [3] Michael Herty, Veronika Sachers . Adjoint calculus for optimization of gas networks. Networks and Heterogeneous Media, 2007, 2(4): 733-750. doi: 10.3934/nhm.2007.2.733
    [4] Martin Gugat, Falk M. Hante, Markus Hirsch-Dick, Günter Leugering . Stationary states in gas networks. Networks and Heterogeneous Media, 2015, 10(2): 295-320. doi: 10.3934/nhm.2015.10.295
    [5] Mapundi K. Banda, Michael Herty, Axel Klar . Coupling conditions for gas networks governed by the isothermal Euler equations. Networks and Heterogeneous Media, 2006, 1(2): 295-314. doi: 10.3934/nhm.2006.1.295
    [6] Claus Kirchner, Michael Herty, Simone Göttlich, Axel Klar . Optimal control for continuous supply network models. Networks and Heterogeneous Media, 2006, 1(4): 675-688. doi: 10.3934/nhm.2006.1.675
    [7] Fabian Rüffler, Volker Mehrmann, Falk M. Hante . Optimal model switching for gas flow in pipe networks. Networks and Heterogeneous Media, 2018, 13(4): 641-661. doi: 10.3934/nhm.2018029
    [8] Didier Georges . Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems. Networks and Heterogeneous Media, 2009, 4(2): 267-285. doi: 10.3934/nhm.2009.4.267
    [9] Simone Göttlich, Oliver Kolb, Sebastian Kühn . Optimization for a special class of traffic flow models: Combinatorial and continuous approaches. Networks and Heterogeneous Media, 2014, 9(2): 315-334. doi: 10.3934/nhm.2014.9.315
    [10] Gunhild A. Reigstad . Numerical network models and entropy principles for isothermal junction flow. Networks and Heterogeneous Media, 2014, 9(1): 65-95. doi: 10.3934/nhm.2014.9.65

  • The objective of the current examination is to present new sub-classes of q-convex and q-starlike functions inside E={z∈C:|z|<1}, by q-difference operator. We determined connections of these classes and acquired a few fundamental properties, for instance, inclusion relation, subordination properties and q-limits on real part.




    [1] P. L. Duren, Univalent functions, New York: Springer-Verlag, 1983.
    [2] A. W. Goodman, Univalent functions, Washington, New Jersey: Polygonal Publishing House, 1983.
    [3] M. E. H. Ismail, E. Merks, D. Styer, A generalization of starlike functions, Complex Var. Theory Appl., 14 (1990), 77–84. https://doi.org/10.1080/17476939008814407 doi: 10.1080/17476939008814407
    [4] F. H. Jackson, On q-functions and certain difference operators, Trans. Roy. Soc. Edinburgh, 46 (1909), 253–281. https://doi.org/10.1017/S0080456800002751 doi: 10.1017/S0080456800002751
    [5] F. H. Jackson, On q-definite integrals, Quar. J. Pure Appl. Math., 41 (1910), 193–203.
    [6] K. Kuroki, S. Owa, Notes on new class of certain analytic functions, Adv. Math. Sci. J., 1 (2012), 127–131.
    [7] S. S. Miller, P. T. Mocanu, Differential subordination: theory and applications, New York: Marcel Dekker, 2000.
    [8] R. Nadeem, T. Usman, K. S. Nasir, T. Abdeljawad, A new generalization of Mittag-Leffler function via q-calculus, Adv. Differ. Equ., 2020 (2020), 695. https://doi.org/10.1186/s13662-020-03157-z doi: 10.1186/s13662-020-03157-z
    [9] K. I. Noor, S. Riaz, M. A. Noor, On q-Bernardi integral operator, TWMS J. Pure Appl. Math., 8 (2017), 3–11.
    [10] K. I. Noor, Some classes of analytic functions associated with q-Ruscheweyh differential operator, Facta Univ. Ser. Math. Inform., 33 (2018), 531–538.
    [11] A. M. Obad, A. Khan, K. S. Nisar, A. Morsy, q-binomial convolution and transformations of q-Appell polynomials, Axioms, 10 (2021), 1–13. https://doi.org/10.3390/axioms10020070 doi: 10.3390/axioms10020070
    [12] C. Ramachandran, T. Soupramanien, B. A. Frasin, New subclasses of analytic function associated with q-difference operator, Eur. J. Pure Appl. Math., 10 (2017), 348–362.
    [13] Y. J. Sim., O. S. Kwon, On certain classes of convex functions, Int. J. Math. Math. Sci., 2013 (2013), 1–6. https://doi.org/10.1155/2013/294378 doi: 10.1155/2013/294378
    [14] H. M. Srivastava, Q. Z. Ahmad, N. Khan, B. Khan, Hankel andd Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain, Mathematics, 7 (2019), 1–15. https://doi.org/10.3390/math7020181 doi: 10.3390/math7020181

  • This article has been cited by:

    1. Dustin Carrión-Ojeda, Rigoberto Fonseca-Delgado, Israel Pineda, Analysis of factors that influence the performance of biometric systems based on EEG signals, 2021, 165, 09574174, 113967, 10.1016/j.eswa.2020.113967
    2. Leila Farsi, Siuly Siuly, Enamul Kabir, Hua Wang, Classification of Alcoholic EEG Signals Using a Deep Learning Method, 2021, 21, 1530-437X, 3552, 10.1109/JSEN.2020.3026830
    3. Sumair Aziz, Muhammad Umar Khan, Zainoor Ahmad Choudhry, Afeefa Aymin, Adil Usman, 2019, ECG-based Biometric Authentication using Empirical Mode Decomposition and Support Vector Machines, 978-1-7281-2530-5, 0906, 10.1109/IEMCON.2019.8936174
    4. Muhammad Umar Khan, Sumair Aziz, Sara Ibraheem, Aqsa Butt, Hira Shahid, 2019, Characterization of Term and Preterm Deliveries using Electrohysterograms Signatures, 978-1-7281-2530-5, 0899, 10.1109/IEMCON.2019.8936292
    5. Dustin Carrion-Ojeda, Hector Mejia-Vallejo, Rigoberto Fonseca-Delgado, Pilar Gomez-Gil, Manuel Ramirez-Cortes, 2019, A method for studying how much time of EEG recording is needed to have a good user identification, 978-1-7281-5666-8, 1, 10.1109/LA-CCI47412.2019.9037054
    6. Andrei V. Kelarev, Xun Yi, Hui Cui, Leanne Rylands, Herbert F. Jelinek, A survey of state-of-the-art methods for securing medical databases, 2018, 5, 2375-1576, 1, 10.3934/medsci.2018.1.1
    7. Lu-di Wang, Wei Zhou, Ying Xing, Na Liu, Mahmood Movahedipour, Xiao-guang Zhou, A novel method based on convolutional neural networks for deriving standard 12-lead ECG from serial 3-lead ECG, 2019, 20, 2095-9184, 405, 10.1631/FITEE.1700413
    8. Qingxue Zhang, Dian Zhou, Xuan Zeng, 2017, Hear the heart: Daily cardiac health monitoring using Ear-ECG and machine learning, 978-1-5386-1104-3, 448, 10.1109/UEMCON.2017.8249110
    9. Yaroslav Voznyi, Mariia Nazarkevych, Volodymyr Hrytsyk, Nataliia Lotoshynska, Bohdana Havrysh, DESIGN OF BIOMETRIC PROTECTION AUTHENTIFICATION SYSTEM BASED ON K-AVERAGE METHOD, 2021, 4, 2663-4023, 85, 10.28925/2663-4023.2021.12.8595
    10. Mariya Nazarkevych, Yaroslav Voznyi, Volodymyr Hrytsyk, Ivanna Klyujnyk, Bohdana Havrysh, Nataliia Lotoshynska, 2021, Identification of Biometric Images by Machine Learning, 978-1-6654-4296-1, 95, 10.1109/ELIT53502.2021.9501064
    11. Ömer Kasim, Mustafa Tosun, Biometric Authentication from Photic Stimulated EEG Records, 2021, 35, 0883-9514, 1407, 10.1080/08839514.2021.1981660
    12. Fatma Mallouli, Nesrine Khelifi, Aya Hellal, Imen Ferjani, Nada Chaabane, Mejda Dakhlaoui, Houda Chamakhi, 2023, Biometric Authentification Comparison: Toward Secure Human Recognition, 979-8-3503-6151-3, 1264, 10.1109/CSCI62032.2023.00206
    13. Ilija Tanasković, Ljiljana B. Lazarević, Goran Knežević, Nikola Milosavljević, Olga Dubljević, Bojana Bjegojević, Nadica Miljković, CardioPRINT: Biometric identification based on the individual characteristics derived from the cardiogram, 2025, 265, 09574174, 126018, 10.1016/j.eswa.2024.126018
    14. Vinodhini Chinnayan Meiyalagan, Sabeenian Royappan Savarimuthu, 2025, 3279, 0094-243X, 020170, 10.1063/5.0263047
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.1

Metrics

Article views(1937) PDF downloads(78) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog