A Note on Linear Multiplier Fractional \(q\)-Differintegral Operator With Varying Arguments
DOI:
https://doi.org/10.26713/cma.v16i1.2965Keywords:
Analytic function, Univalent function, Fractional \(q\)-differintegral operator, \(q\)-Bernardi operatorAbstract
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.
Downloads
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.



