A Note on Linear Multiplier Fractional \(q\)-Differintegral Operator With Varying Arguments

Authors

  • Rmsen Abdulbari Ali Ahmed Department of Mathematics, Taiz University, Taiz, Yemen https://orcid.org/0009-0004-1989-9295
  • N. Ravikumar JSS College of Arts Commerce and Science, University of Mysore, Mysuru 570025, Karnataka, India

DOI:

https://doi.org/10.26713/cma.v16i1.2965

Keywords:

Analytic function, Univalent function, Fractional \(q\)-differintegral operator, \(q\)-Bernardi operator

Abstract

 We introduce new subclasses of analytic functions with varying arguments by making use of linear multiplier fractional \(q\)-differintegral operator. For functions belonging to these classes, we obtain coefficient estimates, distortion theorems, extreme points, \(q\)-Bernardi integral operator, and many more properties.

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References

M. K. Aouf, A. O. Mostafa, A. Shamandy and E. A. Adwan, Some properties for certain class of analytic functions with varying arguments, International Journal of Analysis 2013(1) (2013), 380938, DOI: 10.1155/2013/380938.

M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Subordination results for certain classes of analytic functions defined by convolution with complex order, Bulletin of Mathematical Analysis and Applications 3(1) (2011), 61 – 68, URL: https://www.emis.de/journals/BMAA/repository/docs/BMAA3-1-8.pdf.

M. P. Chen, On functions satisfying Re{f (z)/z} > α, Tamkang Journal of Mathematics 5 (1974), 231 – 234.

M. P. Chen, On the regular functions satisfying Re{f (z)/z} > α, Bulletin of the Institute of Mathematics. Academia Sinica 3(1) (1975), 65 – 70.

C. Chunyi and S. Owa, Certain class of analytic functions in the unit disk, Kyungpook Mathematical Journal 33(1) (1993), 13 – 23, URL: https://www.koreascience.kr/article/JAKO199325748114626.pdf.

G. Gasper and M. Rahman, Basic hypergeometric series, in: Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, pp. 1 – 35, (2004), DOI: 10.1017/cbo9780511526251.004.

R. M. Goel, On functions satisfying Re{f (z)/z} > α, Publicationes Mathematicae Debrecen 18 (1971), 111 – 117.

W. Janowski, Some extremal problems for certain families of analytic functions I, Annales Polonici Mathematici 3(28) (1973), 297 – 326, DOI: 10.4064/ap-28-3-297-326.

F. H. Jackson, XI. – On q-functions and a certain difference operator, Earth and Environmental Science Transactions of the Royal Society of Edinburgh 46(2) (1909), 253 – 281, DOI: 10.1017/S0080456800002751.

K. I. Noor, S. Riaz and M. A. Noor, On q-Bernardi integral operator, TWMS Journal of Pure and Applied Mathematics 8(1) (2017), 3 – 11.

S. D. Purohit and R. K. Raina, Certain subclasses of analytic functions associated with fractional qcalcurmlus operators, Mathematica Scandinavica 109 (2011), 55 – 70, DOI: 10.7146/math.scand.a-15177.

N. Ravikumar, Certain classes of analytic functions defined by fractional q-calculus operator, Acta Universitatis Sapientiae, Mathematica 10(1) (2018), 178 – 188, DOI: 10.2478/ausm-2018-0015.

H. Silverman, Univalent functions with varying arguments, Houston Journal of Mathematics 7(2) (1981), 283 – 287.

H. M. Srivastava and S. Owa, Certain classes of analytic functions with varying arguments, Journal of Mathematical Analysis and Applications 136(1) (1988), 217 – 228, DOI: 10.1016/0022-247x(88)90127-8.

S. Sivasubramanian, A. Mohammed and M. Darus, Certain subordination properties for subclasses of analytic functions involving complex order, Abstract and Applied Analysis 2011(1) (2011), 375897, DOI: 10.1155/2011/375897.

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Published

01-07-2025
CITATION

How to Cite

Ahmed, R. A. A., & Ravikumar, N. (2025). A Note on Linear Multiplier Fractional \(q\)-Differintegral Operator With Varying Arguments. Communications in Mathematics and Applications, 16(1), 327–337. https://doi.org/10.26713/cma.v16i1.2965

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Section

Research Article