Research Article
Year 2020,
Volume: 41 Issue: 3, 625 - 634, 30.09.2020
Abstract
The main purpose of the present paper is to determine the radii of lemniscate starlikeness, lemniscate convexity, Janowski starlikeness and Janowski convexity of normalized Wright functions. The key tools in the proof of our main results are the infinite product representation of Wright function and some properties of real zeros of the Wright function and its derivative.
Keywords
Wright function radii of Lemniscate starlikeness and convexity radii of Janowski starlikeness and convexity
References
- Aktaş, İ. and Baricz, Á., Bounds for radii of starlikeness of some q-Bessel functions, Results Math., 72(1-2) (2017) 947-963.
- Aktaş, İ., Baricz, Á. and Orhan H., Bounds for the radii of starlikeness and convexity of some special functions, Turk J Math, 42(1) (2018) 211–226.
- Aktaş, İ., Baricz, Á. and Yağmur, N., Bounds for the radii of univalence of some special functions, Math. Inequal. Appl., 20(3) (2017) 825–843.
- Aktaş, İ., Baricz, Á. and Singh, S., Geometric and monotonic properties of hyper-Bessel functions, Ramanujan J., 51(2) (2020) 275-295.
- Aktaş İ., Toklu, E. and Orhan, H., Radii of uniform convexity of some special functions, Turk J Math, 42(6) (2018) 3010-3024.
- Ali, R.M., Jain, N.K. and Ravichandran, V., Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput., 218(11) (2012) 6557–6565.
- Baricz, Á. and Prajapati, A., Radii of starlikeness and convexity of generalized Mittag-Leffler functions, Math. Commun., 25 (2020) 117-135.
- Baricz, Á. and Szász, R., The radius of convexity of normalized Bessel functions of the first kind, Anal. Appl., 12(5) (2014) 485-509.
- Baricz, Á., Toklu, E. and Kadıoğlu, E., Radii of starlikeness and convexity of Wright functions., Math. Commun., 23 (2018) 97-117.
- Goodman, A.W., Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983.
- Gorenflo, R., Luchko, Y. and Mainardi, F., Analytical properties and applications of the Wright function, Fract. Calc. Appl. Anal., 2(4) (1999) 383-414.
- Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23 (1970/1971) 159–177.
- Madaan, V., Kumar, A. and Ravichandran, V., Lemniscate Convexity and Other Properties of Generalized Bessel Functions, Stud. Sci. Math. Hun., 56(4) (2019) 404-419.
- Madaan, V., Kumar, A. and Ravichandran, V., Radii of starlikeness and convexity of Some Entire Functions, Bull. Malays. Math. Sci. Soc., (2020).
- Sokól, J. and Stankiewicz, J., Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat., 19 (1996) 101–105.
- Toklu, E., Radii of starlikeness and convexity of q-Mittag-Leffler functions, Turk J Math, 43(5) (2019) 2610-2630.
- Toklu, E., Aktaş, İ. and Orhan, H., Radii problems for normalized q-Bessel and Wright functions, Acta Univ Sapientiae Mathematica, 11(1) (2019) 203-223.
- Verma, S. and Ravichandran, V., Radius problems for ratios of Janowski starlike functions with their derivatives, Bull. Malays. Math. Sci. Soc., 40(2) (2017) 819–840.
- Wright, E.M., On the coefficients of power series having exponential singularities, J. Lond. Math. Soc., (1933) 71-79.
Year 2020,
Volume: 41 Issue: 3, 625 - 634, 30.09.2020
Abstract
References
- Aktaş, İ. and Baricz, Á., Bounds for radii of starlikeness of some q-Bessel functions, Results Math., 72(1-2) (2017) 947-963.
- Aktaş, İ., Baricz, Á. and Orhan H., Bounds for the radii of starlikeness and convexity of some special functions, Turk J Math, 42(1) (2018) 211–226.
- Aktaş, İ., Baricz, Á. and Yağmur, N., Bounds for the radii of univalence of some special functions, Math. Inequal. Appl., 20(3) (2017) 825–843.
- Aktaş, İ., Baricz, Á. and Singh, S., Geometric and monotonic properties of hyper-Bessel functions, Ramanujan J., 51(2) (2020) 275-295.
- Aktaş İ., Toklu, E. and Orhan, H., Radii of uniform convexity of some special functions, Turk J Math, 42(6) (2018) 3010-3024.
- Ali, R.M., Jain, N.K. and Ravichandran, V., Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput., 218(11) (2012) 6557–6565.
- Baricz, Á. and Prajapati, A., Radii of starlikeness and convexity of generalized Mittag-Leffler functions, Math. Commun., 25 (2020) 117-135.
- Baricz, Á. and Szász, R., The radius of convexity of normalized Bessel functions of the first kind, Anal. Appl., 12(5) (2014) 485-509.
- Baricz, Á., Toklu, E. and Kadıoğlu, E., Radii of starlikeness and convexity of Wright functions., Math. Commun., 23 (2018) 97-117.
- Goodman, A.W., Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983.
- Gorenflo, R., Luchko, Y. and Mainardi, F., Analytical properties and applications of the Wright function, Fract. Calc. Appl. Anal., 2(4) (1999) 383-414.
- Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23 (1970/1971) 159–177.
- Madaan, V., Kumar, A. and Ravichandran, V., Lemniscate Convexity and Other Properties of Generalized Bessel Functions, Stud. Sci. Math. Hun., 56(4) (2019) 404-419.
- Madaan, V., Kumar, A. and Ravichandran, V., Radii of starlikeness and convexity of Some Entire Functions, Bull. Malays. Math. Sci. Soc., (2020).
- Sokól, J. and Stankiewicz, J., Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat., 19 (1996) 101–105.
- Toklu, E., Radii of starlikeness and convexity of q-Mittag-Leffler functions, Turk J Math, 43(5) (2019) 2610-2630.
- Toklu, E., Aktaş, İ. and Orhan, H., Radii problems for normalized q-Bessel and Wright functions, Acta Univ Sapientiae Mathematica, 11(1) (2019) 203-223.
- Verma, S. and Ravichandran, V., Radius problems for ratios of Janowski starlike functions with their derivatives, Bull. Malays. Math. Sci. Soc., 40(2) (2017) 819–840.
- Wright, E.M., On the coefficients of power series having exponential singularities, J. Lond. Math. Soc., (1933) 71-79.
There are 19 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2020 |
| Submission Date | March 19, 2020 |
| Acceptance Date | August 24, 2020 |
| Published in Issue | Year 2020Volume: 41 Issue: 3 |