Partial sums of generalized Lommel-Wright function
Authors
B. A. Frasin
- Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan.
I. Aldawish
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
S. Kazımoglu
- Department of Mathematics, Faculty of Science and Letters, Kafkas University, Campus, 36100 Kars, Turkey.
Abstract
In the present study, our main aim is to give lower bounds for the ratio of
the normalized Lommel-Wright function and their sequences of partial sums,
as well as for the quotients of the derivative of normalized Lommel-Wright
function and their partial sums. In addition, some applications related to the
obtained results are also given. Given the significance of these results, their
geometric interpretation of the image domain is also included.
Share and Cite
ISRP Style
B. A. Frasin, I. Aldawish, S. Kazımoglu, Partial sums of generalized Lommel-Wright function, Journal of Mathematics and Computer Science, 40 (2026), no. 1, 73--83
AMA Style
Frasin B. A., Aldawish I., Kazımoglu S., Partial sums of generalized Lommel-Wright function. J Math Comput SCI-JM. (2026); 40(1):73--83
Chicago/Turabian Style
Frasin, B. A., Aldawish, I., Kazımoglu, S.. "Partial sums of generalized Lommel-Wright function." Journal of Mathematics and Computer Science, 40, no. 1 (2026): 73--83
Keywords
- Partial sums
- analytic functions
- generalized Lommel-Wright function
MSC
References
-
[1]
J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math. (2), 17 (1915), 12–22
-
[2]
Á. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73 (2008), 155–178
-
[3]
M. Ça˘ glar, H. Orhan, On neighborhood and partial sums problem for generalized Sakaguchi type functions, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.), 63 (2017), 17–28
-
[4]
M. Ça˘ glar, E. Deniz, Partial sums of the normalized Lommel functions, Math. Inequal. Appl., 18 (2015), 1189–1199
-
[5]
E. Deniz, H. Orhan, Some properties of certain subclasses of analytic functions with negative coefficients by using generalized Ruscheweyh derivative operator, Czechoslovak Math. J., 60(135) (2010), 699–713
-
[6]
E. Deniz, H. Orhan, Certain subclasses of multivalent functions defined by new multiplier transformations, Arab. J. Sci. Eng., 36 (2011), 1091–1112
-
[7]
M. B. M. De Oteiza, S. Kalla, S. Conde, Un estudio sobre la función Lommel–Maitland, Rev. Téc. Fac. Ing., Univ. Zulia, 9 (1986), 33–40
-
[8]
M. U. Din, M. Raza, S. Hussain, M. Darus, Certain geometric properties of generalized Dini functions, J. Funct. Spaces, 2018 (2018), 9 pages
-
[9]
B. A. Frasin, Generalization of partial sums of certain analytic and univalent functions, Appl. Math. Lett., 21 (2008), 735–741
-
[10]
B. A. Frasin, Partial sums of certain analytic and univalent functions, Acta Math. Acad. Paedagog. Nyházi, 21 (2005), 135–145
-
[11]
B. A. Frasin, Partial sums of generalized Rabotnov function, Bol. Soc. Mat. Mex. (3), 29 (2023), 13 pages
-
[12]
B. A. Frasin, Univalence of some integral operators involving Rabotnov fractional exponential function, Zh. Sib. Fed. Univ. Mat. Fiz., 17 (2024), 710–720
-
[13]
B. A. Frasin,; L.-I. Cotîrl˘a, Partial Sums of the Normalized Le Roy-Type Mittag-Leffler Function, Axioms, 12 (2023), 12 pages
-
[14]
A. W. Goodman, Univalent functions. Vol. I, Mariner Publishing Co., Tampa, FL (1984)
-
[15]
B.-N. Guo, F. Qi, Refinements of lower bounds for polygamma functions, Proc. Amer. Math. Soc., 141 (2013), 1007–1015
-
[16]
S. Kazımo˘ glu, Partial sums of the Miller-Ross function, Turk. J. Sci., 6 (2021), 167–173
-
[17]
S. Kazımo˘ glu, E. Deniz, Partial sums of the Rabotnov function, Acta Univ. Sapientiae Math., 14 (2022), 250–261
-
[18]
A. A. Kilbas, M. Saigo, J. J. Trujillo, On the generalized Wright function, Fract. Calc. Appl. Anal., 5 (2002), 437–460
-
[19]
A. Laforgia, Further inequalities for the gamma function, Math. Comp., 42 (1984), 597–600
-
[20]
L.-J. Lin, S. Owa, On partial sums of the Libera integral operator, J. Math. Anal. Appl., 213 (1997), 444–454
-
[21]
L. Lorch, Inequalities for ultraspherical polynomials and the gamma function, J. Approx. Theory, 40 (1984), 115–120
-
[22]
S. S. Miller, P. T. Mocanu, Univalence of Gaussian and confluent hypergeometric functions, Proc. Amer. Math. Soc., 110 (1990), 333–342
-
[23]
H. Orhan, N. Ya˘gmur, Partial sums of generalized Bessel functions, J. Math. Inequal., 8 (2014), 863–877
-
[24]
S. Owa, H. M. Srivastava, N. Saito, Partial sums of certain classes of analytic functions, Int. J. Comput. Math., 81 (2004), 1239–1256
-
[25]
R. S. Pathak, Certain convergence theorems and asymptotic properties of a generalization of Lommel and Maitland transformations, Proc. Natl. Acad. Sci. India Sect. Phys. Sci., A-36 (1966), 81–86
-
[26]
J. K. Prajapat, Certain geometric properties of the Wright function, Integral Transforms Spec. Funct., 26 (2015), 203–212
-
[27]
M. Raza, M. U. Din, Close-to-convexity of q-Mittag-Leffler functions, C. R. Acad. Bulgare Sci., 71 (2018), 1581–1591
-
[28]
T. Sheil-Small, A note on partial sums of convex schlicht functions, Bull. London Math. Soc., 2 (1970), 165–168
-
[29]
H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl., 209 (1997), 221–227
-
[30]
H. Silverman, Partial sums of a class of univalent functions, Tamkang J. Math., 29 (1998), 171–174
-
[31]
E. M. Silvia, On partial sums of convex functions of order α, Houston J. Math., 11 (1985), 397–404
-
[32]
S. Sümer Eker, S. Ece, Geometric properties of normalized Rabotnov function, Hacet. J. Math. Stat., 51 (2022), 1248–1259
-
[33]
M. S. Ur Rehman, Q. Z. Ahmad, H. M. Srivastava, B. Khan, N. Khan, Partial sums of generalized q-Mittag-Leffler functions, AIMS Math., 5 (2020), 408–420
-
[34]
N. Ya˘gmur, Hardy space of Lommel functions, Bull. Korean Math. Soc., 52 (2015), 1035–1046
-
[35]
N. Ya˘gmur, H. Orhan, Starlikeness and convexity of generalized Struve functions, Abstr. Appl. Anal., 2013 (2013), 6 pages
-
[36]
N. Ya˘gmur, H. Orhan, Partial sums of generalized Struve functions, Miskolc Math. Notes, 17 (2016), 657–670
-
[37]
H. M. Zayed, K. Mehrez, Generalized Lommel-Wright function and its geometric properties, J. Inequal. Appl., 2022 (2022), 24 pages