Mapping Properties of a Generalized Integral Operator Involving Some Special Functions

Anuradha Vishnoi; Arvind Kumar Sharma; Saurabh Porwal

doi:10.47000/tjmcs.1709887

Mapping Properties of a Generalized Integral Operator Involving Some Special Functions

Abstract

The primary goal of the present article is to introduce a generalized integral operator involving with Bessel functions of first kind, Mittag-Leffler and generalized Struve functions. Further, we determine some sufficient condition for this integral operator belonging to certain subclasses of starlike functions. Our results generalize the some results of [21,23].

Keywords

References

Baricz, A., Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73(1-2)(2008), 155–178.
Baricz, A., Generalized Bessel Functions of the First Kind, Lecture Notes in Mathematics, 1994, Springer-Verlag, Berlin, 2010.
Baricz, A., Frasin, B.A., Univalence of integral operators involving Bessel functions, Appl. Math. Lett., 23(4)(2010), 371–376.
Bieberbach, L., Uber die koeffizienten derjenigen Potenzreihen, Welchecine Schlichte Abbildung des Einheitrakseises Vermittein, S.B. Preuss, Akad, Wiss, 138(1916), 940–955.
Branges, L.D., A proof of the Bieberbach Conjecture, Acta Math., 154(1985), 137–152.
Deniz, E., Orhan, H., Srivastava, H.M., Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2011), 883–917.
Din, M.U., Raza, M., Deniz, E., Univalence criteria for general integral operators involving normalized Dini functions, Filomat, 34(7)(2020), 2203–2216.
Din, M.U., Srivastava, H.M., Raza, M., Univalence of certain integral operators involving generalized Struve functions, Hacettepe J. Math. Stat., 47(4) (2018), 821–833.

Dixit, P., Porwal, S., Singh, M.K., Starlikeness of an integral operator associated with Mittag-Leffler functions, Int. J. Nonlinear Anal. Appl., 14(2023) 5, 1—7.
Frasin, B.A., Sufficient condition for integral operator defined by Bessel functions, J. Math. Inequal., 4(3)(2010), 301–306.
Frasin, B.A., Aldawish, I., On subclasses of uniformly Spiral-like functions associated with generalized Bessel functions, J. Function Spaces, 2019(2019), Article ID 1329462, 1–6.
Magesh, N., Porwal, S., Singh, S.P., Some geometric properties of an integral operator involving Bessel functions, Novi Sad J. Math., 47(2)(2017), 149–156.
Mittag-Leffler, G. M., Sur la nouvelle function E(x), C. R. Acad. Sci. Paris, 137(1903), 554–558.
Murugusundaramoorthy, G., Vijaya, K., Kasthuri, M., A note on subclasses of starlike and convex functions associated with Bessel functions, J. Nonlinear Funct. Anal., 2014(2014), Article ID 11, 1–11.
Orhan, H., Yagmur, N., Geometric properties of generalized Struve functions, An. Stiint. Univ. Al. I. Cuza Iasi.Mat., (N.S.), 63(2)(2017), 229–244.
Oros, G.I., Oros, G., Bardac-Vlada,D.A., Study on the criteria for starlikeness in integral operators involving Bessel functions, Symmetry, 15(11)(2023), 1976.
Park, J.H., Srivastava, H.M., Cho, N.E., Univalence and convexity conditions for certain integral operators associated with the Lommel function of the first kind, Aims Mathematics, 6(10)(2021), 11380–11402.
Porwal, Saurabh, Ahmad, M., Some sufficient condition for generalized Bessel functions associated with conic regions, Vietnam J. Math., 43(2015), 163–172.
Porwal, Saurabh, Breaz, D., Mapping properties of an integral operator involving Bessel functions, Analytic Number Theory, Approximation Theory and Spect. Funct., 821-826, Springer, New York, 2014.
Porwal, Saurabh, Kumar, M., Mapping properties of an integral operator involving Bessel functions on some subclasses of univalent functions, Afr. Mat., 28(1-2)(2017), 165–170
Porwal, Saurabh, Magesh, N., Geometric properties of an integral operator associated with Mittag-Leffler functions, Bol. Soc. Paran. Math., 42(2024), 1–7.
Porwal, Saurabh, Murugusundaramoorthy, G., Geometric properties of a new integral operator associated with Dini functions, Electronic J. Math. Anal. Appl., 10(2)(2022), 267–274.
Porwal, Saurabh, Gupta, A., Murugusundaramoorthy, G., New sufficient conditions for starlikeness of certain integral operators involving Bessel functions, Acta Univ. Matthiae Belii series Mathematics, 25(2017), 79–87.
Raza, M., Yagmur, N., Some properties of a class of analytic functions defined by generalized Struve functions, Turkish J. Math., 39(6)(2015), 931–944.
Raza, M., Noreen, S., Malik, S.N., Geometric properties of integral operators defined by Bessel functions, J. Ineq. Spec. Funct., 7(2016), 34–48.
Robertson, M.S., On the theory of univalent functions, Annals of Math., 37(1936), 374–408.
Selvakumaran, K.A., Szasz, R., Certain geometric properties of an integral operator involving Bessel functions, Kyungpook Math. J., 58(3)(2018), 507-517.
Shiraishi, H.,Owa, S., Starlikeness and convexity for analytic functions concerned with Jack’s Lemma, International J. Open Problem Compute. Math., 2(1)(2009), 37–47.
Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109–116.
Srivastava, H. M., Frasin, B. A., Pescar, V., Univalance of integral operators involving Mittag-Leffler functions, Appl. Math. Inf. Sci., 11(3)(2017), 635-641.
Struve, H., Beitrag zur Theeorie der diffraction an Fernro heren, Annalen der Physik and Chemie, 17(13)(1882), 1008–1016.
Szasz, R., Kupan, P., About the univalence of the Bessel functions, Stud. Univ. Babes-Bolyai Math., 54(1), (2009), 127–132.
Ularu, N., The univalence of some integral operators using the Bessel functions, Math. Bech., 65(4)(2013), 547–554.
Wiman, A., Über den fundamental satz in der Theorie der Funcktionen E(x), Acta Math., 29(1905), 191–201.
Wiman, A., Über die Nullstellum der Funcktionen E(x), Acta Math., 29(1905), 217–234.
Yagmur, N., Orhan, H., Starlikeness and convexity of generalized Struve functions, Abstract Appl. Anal., 2013(2013), Art ID 954513, 1–6.

Details

Primary Language

English

Subjects

Real and Complex Functions (Incl. Several Variables)

Journal Section

Research Article

Authors

Anuradha Vishnoi
0009-0004-2283-0934
India

Arvind Kumar Sharma
0009-0000-5351-5241
India

Saurabh Porwal ^*
0000-0003-0847-3550
India

Publication Date

June 30, 2026

Submission Date

May 31, 2025

Acceptance Date

December 28, 2025

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1709887

IZ

https://izlik.org/JA79WX56YF

Cite

RIS / Bibtex

APA

Vishnoi, A., Sharma, A. K., & Porwal, S. (2026). Mapping Properties of a Generalized Integral Operator Involving Some Special Functions. Turkish Journal of Mathematics and Computer Science, 18(2), 332-340. https://doi.org/10.47000/tjmcs.1709887

AMA

1.Vishnoi A, Sharma AK, Porwal S. Mapping Properties of a Generalized Integral Operator Involving Some Special Functions. TJMCS. 2026;18(2):332-340. doi:10.47000/tjmcs.1709887

Chicago

Vishnoi, Anuradha, Arvind Kumar Sharma, and Saurabh Porwal. 2026. “Mapping Properties of a Generalized Integral Operator Involving Some Special Functions”. Turkish Journal of Mathematics and Computer Science 18 (2): 332-40. https://doi.org/10.47000/tjmcs.1709887.

EndNote

Vishnoi A, Sharma AK, Porwal S (June 1, 2026) Mapping Properties of a Generalized Integral Operator Involving Some Special Functions. Turkish Journal of Mathematics and Computer Science 18 2 332–340.

IEEE

[1]A. Vishnoi, A. K. Sharma, and S. Porwal, “Mapping Properties of a Generalized Integral Operator Involving Some Special Functions”, TJMCS, vol. 18, no. 2, pp. 332–340, June 2026, doi: 10.47000/tjmcs.1709887.

ISNAD

Vishnoi, Anuradha - Sharma, Arvind Kumar - Porwal, Saurabh. “Mapping Properties of a Generalized Integral Operator Involving Some Special Functions”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 332-340. https://doi.org/10.47000/tjmcs.1709887.

JAMA

1.Vishnoi A, Sharma AK, Porwal S. Mapping Properties of a Generalized Integral Operator Involving Some Special Functions. TJMCS. 2026;18:332–340.

MLA

Vishnoi, Anuradha, et al. “Mapping Properties of a Generalized Integral Operator Involving Some Special Functions”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 332-40, doi:10.47000/tjmcs.1709887.

Vancouver

1.Anuradha Vishnoi, Arvind Kumar Sharma, Saurabh Porwal. Mapping Properties of a Generalized Integral Operator Involving Some Special Functions. TJMCS. 2026 Jun. 1;18(2):332-40. doi:10.47000/tjmcs.1709887