Geometric admissibility of hypergeometric and integral operators for the synthesis of digital filters

Authors

  • R. Kamali
    Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, India
  • S. Prema
    Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, India

Keywords:

Harmonic mappings, Uniformly convex functions, Gaussian hypergeometric functions, Integral operators, Digital filter design

Abstract

In this study, rigorous analytical criteria are developed to determine when the Gaussian hypergeometric function belongs to the Sakaguchi-type class P(delta, sigma,t). A computable sufficient condition is established in Theorem 2.1, and the associated integral operator G( lambda, mu; nu; z) is shown to satisfy the admissibility conditions for membership in P(delta, sigma,t) under the stated parameter assumptions. These theoretical results are interpreted in the context of digital filter synthesis through an admissibility-based design framework. The proposed approach provides a systematic procedure for selecting admissible parameter values that satisfy the required geometric conditions for filter construction. Numerical examples, including admissibility contour maps and frequency-response characteristics, illustrate the proposed framework and demonstrate its potential for digital filter design based on geometric function theory.

Dimensions

[1] P. Murugabharathi & B. Srutha Keerthi, ``Properties of unified class in terms of hypergeometric functions'', Journal of Pharmaceutical Negative Results 13 (2022) 3853. https://www.pnrjournal.com/index.php/home/article/view/9566.

[2] K. Suchithra, B. A. Stephen, A. Gangadharan & S. Sivasubramanian, ``Some properties of hypergeometric functions for a certain subclass of uniformly convex functions'', International Journal of Pure and Applied Mathematics 43 (2008) 485.

[3] F. Rønning, ``On starlike functions associated with parabolic regions'', Annales Universitatis Mariae Curie-Skłodowska, Sectio A 45 (1991) 117. https://bc.umcs.pl/dlibra/publication/34437/edition/31232/content.

[4] W. Ma & D. Minda, ``Uniformly convex functions'', Annales Polonici Mathematici 57 (1992) 165. https://doi.org/10.4064/ap-57-2-165-175.

[5] A. W. Goodman, ``On uniformly convex functions'', Annales Polonici Mathematici 56 (1991) 87. https://doi.org/10.4064/ap-56-1-87-92.

[6] F. Rønning, ``Uniformly convex functions and a corresponding class of starlike functions'', Proceedings of the American Mathematical Society 118 (1993) 189. https://doi.org/10.1090/S0002-9939-1993-1128729-7.

[7] N. P. Damodaran & B. Srutha Keerthi, ``Properties of hypergeometric functions for functions certain subclasses of Sakaguchi type functions'', International Journal of Recent Technology and Engineering 7 (2019) 491. https://www.ijrte.org/portfolio-item/ES2191017519/.

[8] B. Srutha Keerthi, B. A. Stephen, A. Gangadharan & S. Sivasubramanian, ``Some properties of hypergeometric functions for certain subclasses of starlike functions'', Indian Journal of Mathematics 50 (2008) 495. https://www.amsallahabad.org/pdf/ijm503.pdf.

[9] M. Ibrahim & K. R. Karthikeyan, ``Unified solution of some properties related to $lambda$-pseudo starlike functions'', Contemporary Mathematics 4 (2023) 926. https://doi.org/10.37256/cm.4420232366.

[10] E. Merkes & B. T. Scott, ``Starlike hypergeometric functions'', Proceedings of the American Mathematical Society 12 (1961) 885. https://doi.org/10.2307/2034382.

[11] S. Ruscheweyh & V. Singh, ``On the order of starlikeness of hypergeometric functions'', Journal of Mathematical Analysis and Applications 113 (1986) 1. https://doi.org/10.1016/0022-247X(86)90329-X.

[12] B. C. Carlson & D. B. Shaffer, ``Starlike and prestarlike hypergeometric functions'', SIAM Journal on Mathematical Analysis 15 (1984) 737. https://doi.org/10.1137/0515057.

[13] H. Silverman, ``Starlike and convexity properties for hypergeometric functions'', Journal of Mathematical Analysis and Applications 172 (1993) 574. https://doi.org/10.1006/jmaa.1993.1044.

[14] A. V. Oppenheim & R. W. Schafer, Discrete-Time Signal Processing, 3rd ed., Prentice Hall, Upper Saddle River, NJ, USA, 2010. https://www.pearson.com/en-us/subject-catalog/p/discrete-time-signal-processing/P200000003226/9780131988422.

[15] R. Bharati, R. Parvatham & A. Swaminathan, ``On subclasses of uniformly convex functions and a corresponding class of starlike functions'', Tamkang Journal of Mathematics 28 (1997) 17. https://doi.org/10.5556/j.tkjm.28.1997.4330.

[16] J. G. Proakis & D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, 4th ed., Prentice Hall, Upper Saddle River, NJ, USA, 2007. https://search.worldcat.org/title/Digital-signal-processing/oclc/62804704.

[17] R. Kamali, S. Prema, A. S. A. Shrikaanth, V. Govindan & M. Donganont, ``Image edge detection enhancement using coefficient estimates for classes of quasi-subordination: Fekete--Szego problems'', European Journal of Pure and Applied Mathematics 18 (2025) 6632. https://doi.org/10.29020/nybg.ejpam.v18i4.6632.

[18] B. Srutha Keerthi & S. Prema, ``Coefficient problem for certain classes of analytic functions using Hankel determinant'', International Journal of Innovative Technology and Exploring Engineering 8 (2019) 301. https://doi.org/10.35940/ijitee.J1054.08810S19.

[19] S. Prema & B. Srutha Keerthi, ``Coefficient estimates for certain subclasses of meromorphic bi-univalent functions'', Asia Life Sciences, Supplement 14 (2017) 181.

[20] A. Saliu & S. O. Oladejo, ``On lemniscate of Bernoulli of $q$-Janowski type'', Journal of the Nigerian Society of Physical Sciences 4 (2022) 961. https://doi.org/10.46481/jnsps.2022.961.

[21] R. O. Ayinla & A. O. Lasode, ``Estimates for a class of analytic and univalent functions connected with quasi-subordination'', Proceedings of the Nigerian Society of Physical Sciences 1 (2024) 82. https://doi.org/10.61298/pnspsc.2024.1.82.

[22] S. Owa, T. Sekine & R. Yamakawa, ``On Sakaguchi-type functions'', Applied Mathematics and Computation 187 (2007) 356. https://doi.org/10.1016/j.amc.2006.08.133.

[23] A. O. Mostafa, ``Starlikeness and convexity results for hypergeometric functions'', Computers & Mathematics with Applications 59 (2010) 2821. https://doi.org/10.1016/j.camwa.2010.01.053.

[24] M. K. Aouf, A. O. Mostafa & H. M. Zayed, ``Some properties of uniformly starlike and convex hypergeometric functions'', Azerbaijan Journal of Mathematics 9 (2019) 2. https://www.azjm.org/volumes/0902/pdf/0902-1.pdf.

[25] M. K. Aouf, A. O. Mostafa & H. M. Zayed, ``Necessity and sufficiency for hypergeometric functions to be in a subclass of analytic functions'', Journal of the Egyptian Mathematical Society 23 (2015) 476. https://doi.org/10.1016/j.joems.2015.01.002.

[26] N. E. Cho, S. Y. Woo & S. Owa, ``Uniform convexity properties for hypergeometric functions'', Fractional Calculus and Applied Analysis 5 (2002) 303.

[27] O. S. Kwon & N. E. Cho, ``Starlike and convex properties for hypergeometric functions'', International Journal of Mathematics and Mathematical Sciences 2008 (2008) 159029. https://doi.org/10.1155/2008/159029.

[28] W. Cauer, Synthesis of Linear Communication Networks, McGraw--Hill, New York, USA, 1958. https://openlibrary.org/books/OL18959038M/Synthesis_of_linear_communication_networks.

[29] S. Butterworth, ``On the theory of filter amplifiers'', Wireless Engineer 7 (1930) 536. https://cir.nii.ac.jp/crid/1370869854360999320.

[30] A. I. Zverev, Handbook of Filter Synthesis, John Wiley & Sons, New York, USA, 1967. https://www.wiley-vch.de/en/areas-interest/engineering/handbook-of-filter-synthesis-978-0-471-74942-4.

[31] J. Sokół, ``On some applications of the Dziok--Srivastava operator'', Applied Mathematics and Computation 201 (2008) 774. https://doi.org/10.1016/j.amc.2008.01.013.

fig 1

Published

2026-08-11

How to Cite

Geometric admissibility of hypergeometric and integral operators for the synthesis of digital filters. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3609. https://doi.org/10.46481/jnsps.2026.3609

Issue

Volume 8, Issue 3, August 2026 (In Progress)

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 R. Kamali, S. Prema (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Geometric admissibility of hypergeometric and integral operators for the synthesis of digital filters. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3609. https://doi.org/10.46481/jnsps.2026.3609

Similar Articles

1-10 of 106

You may also start an advanced similarity search for this article.