Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator
Abstract
:1. Introduction and Preliminaries
- 1.
- 2.
- 3.
2. The Coefficient Bounds
3. Distortion Bounds and Extreme Points
4. Inclusion Results
5. Partial Sums Results
6. Integral Means Inequalities
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Heinz, E. Über die Lösungen der Minimalflächengleichung, (German). Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. Math.-Phys.-Chem. Abt. 1952, 51–56. [Google Scholar]
- Weitsman, A. On univalent harmonic mappings and minimal surfaces. Pacific J. Math. 2000, 192, 191–200. [Google Scholar] [CrossRef]
- Clunie, J.; Sheil-Small, T. Harmonic univalent functions. Ann. Acad. Aci. Fenn. Ser. A.I. Math. 1984, 9, 3–25. [Google Scholar] [CrossRef]
- Silverman, H. Harmonic univalent functions with negative coefficients. J. Math. Anal. Appl. 1998, 220, 283–289. [Google Scholar] [CrossRef]
- Ahuja, O.P.; Jahangiri, J.M. On a linear combination of classes of multivalently harmonic functions. Kyungpook Math. J. 2002, 42, 61–67. [Google Scholar]
- Abu-muhanna, Y. On harmonic univalent functions. Complex Variables Theory Appl. 1999, 39, 341–348. [Google Scholar] [CrossRef]
- Ahuja, O.P.; Jahangiri, J.M. Sakaguchi-type harmonic univalent functions. Sci. Math. Jpn. 2004, 59, 163–168. [Google Scholar]
- Abu-muhanna, Y.; Lyzzaik, A. The boundary behaviour of harmonic univalent maps. Pacific J. Math. 1990, 141, 1–2. [Google Scholar] [CrossRef]
- Wang, X.-T.; Liang, X.-Q.; Zhang, Y.-L. Precise coefficient estimates for close-to-convex harmonic univalent mappings. J. Math. Anal. Appl. 2001, 263, 501–509. [Google Scholar] [CrossRef]
- Hengartner, W.; Schober, G. Harmonic mappings with given dilatation. J. London Math. Soc. 1986, 33, 473–483. [Google Scholar] [CrossRef]
- Jackson, F.H. On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 1908, 46, 253–281. [Google Scholar] [CrossRef]
- Amini, E.; Al-Omari, S.; Nonlaopon, K.; Baleanu, D. Estimates for coefficients of bi-univalent functions associated with a fractional q-difference operator. Symmetry 2022, 14, 879. [Google Scholar] [CrossRef]
- Aral, A.; Gupta, V.; Agarwal, R.P. Applications of q-Calculus in Operator Theory; Springer: New York, NY, USA, 2013. [Google Scholar]
- Trjitzinsky, W.J. Analytic theory of linear q-difference equations. Acta Math. 1933, 61, 1–38. [Google Scholar] [CrossRef]
- Kiryakova, V. Generalized Fractional Calculus and Applications; Pitman Research Notes in Mathematics; Longman Scientific and Technical: Harlow, UK, 1993; Volume 301. [Google Scholar]
- Kanas, S.; Răducanu, D. Some subclass of analytic functions related to conic domains. Math. Slovaca 2014, 64, 1183–1196. [Google Scholar] [CrossRef]
- Ismail, M.E.H.; Merkes, E.; Styer, D. A generalization of starlike functions. Complex Var. Theory Appl. 1990, 14, 77–84. [Google Scholar] [CrossRef]
- Andrews, G.E.; Askey, G.E.; Roy, R. Special Functions; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar]
- Srivastava, H.M. Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis. Iran. J. Sci. Technol. Trans. A Sci. 2020, 44, 327–344. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Choi, J. Series Associated with the Zeta and Related Functions; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001. [Google Scholar]
- Choi, J.; Srivastava, H.M. Certain families of series associated with the Hurwitz-Lerch Zeta function. Appl. Math. Comput. 2005, 170, 399–409. [Google Scholar] [CrossRef]
- Ferreira, C.; Lopez, J.L. Asymptotic expansions of the Hurwitz-Lerch Zeta function. J. Math. Anal. Appl. 2004, 298, 210–224. [Google Scholar] [CrossRef]
- Garg, M.; Jain, K.; Srivastava, H.M. Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta functions. Integral Transform. Spec. Funct. 2006, 17, 803–815. [Google Scholar] [CrossRef]
- Lin, S.-D.; Srivastava, H.M. Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations. Appl. Math. Comput. 2004, 154, 725–733. [Google Scholar] [CrossRef]
- Lin, S.-D.; Srivastava, H.M.; Wang, P.-Y. Some espansion formulas for a class of generalized Hurwitz-Lerch Zeta functions. Integral Transform. Spec. Funct. 2006, 17, 817–827. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Attiya, A.A. An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. Integral Transform. Spec. Funct. 2007, 18, 207–216. [Google Scholar] [CrossRef]
- Raducanu, D.; Srivastava, H.M. A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch Zeta function. Integral Transform. Spec. Funct. 2007, 18, 933–943. [Google Scholar] [CrossRef]
- Prajapat, J.K.; Goyal, S.P. Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions. J. Math. Inequal. 2009, 3, 129–137. [Google Scholar] [CrossRef]
- Shah, S.A.; Noor, K.I. Study on the q-analogue of a certain family of linear operators. Turk. J. Math. 2019, 43, 2707–2714. [Google Scholar] [CrossRef]
- Hiba, F.A.; Ghanim, F.; Agarwal, P. Geometric studies on inequalities of harmonic functions in a Complex Field Based on ℵ-generalized Hurwitz-Lerch Zeta function. Iran. J. Math. Sci. Inform. 2023, 1, 73–95. [Google Scholar]
- Noor, K.I.; Riaz, S.; Noor, M.A. On q-Bernardi integral operator. TWMS J. Pure Appl. Maths. 2017, 8, 3–11. [Google Scholar]
- Flett, T.M. The dual of an inequality of Hardy and Littlewood and some related inequalities. J. Math. Anal. Appl. 1972, 38, 746–765. [Google Scholar] [CrossRef]
- Ahuja, O.P. Planar harmonic univalent and related mappings. J. Inequal. Pure Appl. Math 2005, 6, 1–18. [Google Scholar]
- Ahuja, O.P.; Jahangiri, J. Noshiro-type harmonic univalent functions. Sci. Math. Jpn. 2002, 56, 1–7. [Google Scholar]
- Silverman, H.; Silvia, E.M. Subclasses of harmonic univalent functions. N. Z. J. Math. 1999, 28, 275–284. [Google Scholar]
- Dziok, J. On Janowski harmonic functions. J. Appl. Anal. 2015, 21, 99–107. [Google Scholar] [CrossRef]
- Jahangiri, J.M.; Silverman, H. Harmonic univalent functions with varying rrguments. Internat. J. Appl. Math. 2002, 8, 267–275. [Google Scholar]
- Jahangiri, J.M. Harmonic functions starlike in the unit disc. J. Math. Anal. Appl. 1999, 235, 470–477. [Google Scholar] [CrossRef]
- Totoi, A.E.; Cotîrlă, L.I. Preserving Classes of Meromorphic Functions through Integral Operators. Symmetry 2022, 14, 1545. [Google Scholar] [CrossRef]
- Jahangiri, J.M.; Murugusundaramoorthy, G.; Vijaya, K. Salagean-Type harmonic univalent functions. Southwest J. Pure Appl. Math. 2002, 2, 77–82. [Google Scholar]
- Jahangiri, J.M.; Murugusundaramoorthy, G.; Vijaya, K. Classes of harmonic starlike functions defined by Sălăgean-type q-differential operators. Hacet. J. Math. Stat. 2020, 49, 416–424. [Google Scholar] [CrossRef]
- Silvia, E.M. On partial Sums of convex functions of order α. Houst. J. Math. 1985, 3, 397–404. [Google Scholar]
- Silverman, H. Partial sums of starlike and convex functions. J. Math. Anal. Appl. 1997, 209, 221–227. [Google Scholar] [CrossRef]
- Porwal, S. Partial sums of certain harmonic univalent functions. Lobachevskii J. Math. 2011, 32, 366–375. [Google Scholar] [CrossRef]
- Porwal, S.; Dixit, K.K. Partial sums of starlike harmonic univalent functions. Kyungpook Math. J. 2010, 50, 433–445. [Google Scholar] [CrossRef]
- Silverman, H. Integral means for univalent functions with negative coefficients. Houston J. Math. 1997, 23, 169–174. [Google Scholar]
- Littlewood, J.E. On inequalities in theory of functions. Proc. Lond. Math. Soc. 1925, 23, 481–519. [Google Scholar] [CrossRef]
- Rekkab, S.; Benhadid, S.; Al-Saphory, R. An Asymptotic Analysis of the Gradient Remediability Problem for Disturbed Distributed Linear Systems. Baghdad Sci. J. 2022, 19, 1623–1635. [Google Scholar] [CrossRef]
- Al-shbeil, I.; Gong, J.; Shaba, T.G. Coefficients Inequalities for the bi-univalent functions related to q-Babalola convolution operator. Fractal Fract. 2023, 7, 155. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Al-Shbeil, I.; Xin, Q.; Tchier, F.; Khan, S.; Malik, S.N. Faber polynomial coefficient estimates for bi-close-to-convex functions defined by the q-fractional derivative. Axioms 2023, 12, 585. [Google Scholar] [CrossRef]
- Faisal, M.I.; Al-Shbeil, I.; Abbas, M.; Arif, M.; Alhefthi, R.K. Problems Concerning Coefficients of Symmetric Starlike Functions Connected with the Sigmoid Function. Symmetry 2023, 15, 1292. [Google Scholar] [CrossRef]
- Al-Shbeil, I.; Gong, J.; Ray, S.; Khan, S.; Khan, N.; Alaqad, H. The properties of meromorphic multivalent q-starlike functions in the Janowski domain. Fractal Fract. 2023, 7, 438. [Google Scholar] [CrossRef]
- Sümer Eker, S.; Murugusundaramoorthy, G.; Şeker, B.; Çekiç, B. Spiral-like functions associated with Miller–Ross-type Poisson distribution series. Bol. Soc. Mat. Mex. 2023, 29, 16. [Google Scholar] [CrossRef]
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Murugusundaramoorthy, G.; Vijaya, K.; Breaz, D.; Cotîrlǎ, L.-I. Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator. Mathematics 2023, 11, 4711. https://doi.org/10.3390/math11234711
Murugusundaramoorthy G, Vijaya K, Breaz D, Cotîrlǎ L-I. Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator. Mathematics. 2023; 11(23):4711. https://doi.org/10.3390/math11234711
Chicago/Turabian StyleMurugusundaramoorthy, Gangadharan, Kaliappan Vijaya, Daniel Breaz, and Luminiţa-Ioana Cotîrlǎ. 2023. "Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator" Mathematics 11, no. 23: 4711. https://doi.org/10.3390/math11234711
APA StyleMurugusundaramoorthy, G., Vijaya, K., Breaz, D., & Cotîrlǎ, L.-I. (2023). Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator. Mathematics, 11(23), 4711. https://doi.org/10.3390/math11234711