Study of the fuzzy $ q- $spiral-like functions associated with the generalized linear operator

A. A. Azzam; Daniel Breaz; Shujaat Ali Shah; Luminiţa-Ioana Cotîrlă; A. A. Azzam; Daniel Breaz; Shujaat Ali Shah; Luminiţa-Ioana Cotîrlă

doi:10.3934/math.20231341

AIMS Mathematics

2023, Volume 8, Issue 11: 26290-26300. doi: 10.3934/math.20231341

Previous Article Next Article

Research article Special Issues

Study of the fuzzy $ q- $spiral-like functions associated with the generalized linear operator

1.
Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt
3.
Department of Mathematics, "1 Decembrie 1918" University of Alba Iulia, Alba Iulia 510009, Romania
4.
Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah 67450, Pakistan
5.
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca 400114, Romania

Received: 12 May 2023 Revised: 08 August 2023 Accepted: 13 August 2023 Published: 14 September 2023
MSC : 30A10, 30C45

Nowadays, the subclasses of analytic functions in terms of fuzzy subsets are studied by various scholars and some of these concepts are extended using the $ q- $theory of functions. In this inspiration, we introduce certain subclasses of analytic function by using the notion of fuzzy subsets along with the idea of $ q- $calculus. We present the $ q- $extensions of the fuzzy spiral-like functions of a complex order. We generalize this class using the $ q- $analogues of the Ruscheweyh derivative and Srivastava-Attiya operators. Various interesting properties are examined for the newly defined subclasses. Also, some previously investigated results are deduced as the corollaries of our major results.
- analytic functions,
- $ q- $spiral-like,
- fuzzy $ q- $starlike functions,
- fuzzy $ q- $convex functions,
- $ q- $Ruscheweyh derivative operator,
- $ q- $Srivastava-Attiya operator
Citation: A. A. Azzam, Daniel Breaz, Shujaat Ali Shah, Luminiţa-Ioana Cotîrlă. Study of the fuzzy $ q- $spiral-like functions associated with the generalized linear operator[J]. AIMS Mathematics, 2023, 8(11): 26290-26300. doi: 10.3934/math.20231341

Related Papers:

Abstract

Nowadays, the subclasses of analytic functions in terms of fuzzy subsets are studied by various scholars and some of these concepts are extended using the $ q- $theory of functions. In this inspiration, we introduce certain subclasses of analytic function by using the notion of fuzzy subsets along with the idea of $ q- $calculus. We present the $ q- $extensions of the fuzzy spiral-like functions of a complex order. We generalize this class using the $ q- $analogues of the Ruscheweyh derivative and Srivastava-Attiya operators. Various interesting properties are examined for the newly defined subclasses. Also, some previously investigated results are deduced as the corollaries of our major results.

References

[1]	L. A. Zadeh, Fuzzy Sets, Inf. Control, 8 (1965), 338–353. http://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[2]	G. I. Oros, G. Oros, The notion of subordination in fuzzy sets theory, Gen. Math., 19 (2011), 97–103.
[3]	S. S. Miller, P. T. Mocanu, Second order-differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 298–305. http://doi.org/10.1016/0022-247X(78)90181-6 doi: 10.1016/0022-247X(78)90181-6
[4]	S. S. Miller, P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28 (1981), 157–171.
[5]	G. I. Oros, G. Oros, Fuzzy differential subordination, Acta Univ. Apulensis, 3 (2012), 55–64.
[6]	I. Dzitac, F. G. Filip, M. J. Manolescu, Fuzzy logic is not fuzzy: World-renowned computer scientist Lotfi A. Zadeh, Int. J. Comput. Commun. Control, 12 (2017), 748–789.
[7]	G. I. Oros, G. Oros, Dominants and best dominants in fuzzy differential subordinations, Stud. Univ. Babes-Bolyai Math., 57 (2012), 239–248.
[8]	G. I. Oros, G. Oros, Briot-Bouquet fuzzy differential subordination, An. Univ. Oradea Fasc. Mat., 19 (2012), 83–87.
[9]	E. A. Haydar, On fuzzy differential subordination, Math. Moravica, 19 (2015), 123–129.
[10]	A. A. Lupas, A note on special fuzzy differential subordinations using generalized Salagean operator and Ruscheweyh derivative, J. Comput. Anal. Appl., 15 (2013), 1476–1483.
[11]	E. Rapeanu, Continuation method for boundary value problems with uniform elliptical operators, J. Sci. Arts, 3 (2011), 273–277.
[12]	A. A. Lupas, A note on special fuzzy differential subordinations using multiplier transformation and Ruschewehy derivative, J. Comput. Anal. Appl., 25 (2018), 1116–1124.
[13]	E. Rapeanu, Approximation by projection of some operators, Analele Universităţii Maritime Constanţa, 11 (2010), 216–218.
[14]	A. K. Wanas, A. H. Majeed, Fuzzy differential subordination properties of analytic functions involving generalized differential operator, Sci. Int., 30 (2018), 297–302.
[15]	A. R. S. Juma, M. H. Saloomi, Generalized Differential Operator on Bistarlike and Biconvex Functions Associated by Quasi-Subordination, J. Phys.: Conf. Ser., 1003 (2018), 012046. http://doi.org/10.1088/1742-6596/1003/1/012046 doi: 10.1088/1742-6596/1003/1/012046
[16]	E. Deniz, M. Çağlar, H. Orhan, The Fekete-Szego problem for a class of analytic functions defined by Dziok-Srivastava operator, Kodai Math. J., 35 (2012), 439–462.
[17]	A. Saha, S. Azami, D. Breaz, E. Rapeanu, S. K. Hui, Evolution for First Eigenvalue of $L_{T, f}$ on an Evolving Riemannian Manifold, Mathematics, 10 (2022), 4614. http://doi.org/10.3390/math10234614 doi: 10.3390/math10234614
[18]	E. A. Totoi, L. I. Cotîrlă, Preserving Classes of Meromorphic Functions through Integral Operators, Symmetry, 14 (2022), 1545. http://doi.org/10.3390/sym14081545 doi: 10.3390/sym14081545
[19]	S. Kazimoğlu, E. Deniz, L. I. Cotîrlă, Geometric Properties of Generalized Integral Operators Related to The Miller–Ross Function, Axioms, 12 (2023), 563. http://doi.org/10.3390/axioms12060563 doi: 10.3390/axioms12060563
[20]	S. A. Shah, E. E. Ali, A. A. Maitlo, T. Abdeljawad, A. M. Albalahi, Inclusion results for the class of fuzzy $\alpha-$convex functions, AIMS Mathematics, 8 (2022), 1375–1383. http://doi.org/10.3934/math.2023069 doi: 10.3934/math.2023069
[21]	K. I. Noor, M. A. Noor, Fuzzy differential subordination involving generalized Noor-Salagean operator, Inf. Sci. Lett., 11 (2022), 1905–1911. http://doi.org/10.18576/isl/110606 doi: 10.18576/isl/110606
[22]	F. M. Sakar, Estimate for Initial Tschebyscheff Polynomials Coefficients on a Certain Subclass of Bi-univalent Functions Defined by Salagean Differential Operator, Acta Univ. Apulensis, 54 (2018), 45–54.
[23]	A. R. S. Juma, A. Al-Fayadh, S. P. Vijayalakshmi, T. V. Sudharsan, Upper bound on the third hankel determinant for the class of univalent functions using an integral operator, Afr. Mat., 33 (2022), 56. http://doi.org/10.1007/s13370-022-00991-0 doi: 10.1007/s13370-022-00991-0
[24]	D. Breaz, K. R. Karthikeyan, E. Umadevi, A. Senguttuvan, Some properties of Bazilevic functions involving Srivastava–Tomovski operator, Axioms, 11 (2022), 687. http://doi.org/10.3390/axioms11120687 doi: 10.3390/axioms11120687
[25]	S. A. Shah, E. E. Ali, A. Catas, A. M. Albalahi, On fuzzy differential subordination associated with $q$-difference operator, AIMS Mathematics, 8 (2023), 6642–6650. http://doi.org/10.3934/math.2023336 doi: 10.3934/math.2023336
[26]	A. F. Azzam, S. A. Shah, A. Alburaikan, S. M. El-Deeb, Certain inclusion properties for the class of $q-$analogue of fuzzy $\alpha-$-convex functions, Symmetry, 15 (2023), 509. http://doi.org/10.3390/sym15020509 doi: 10.3390/sym15020509
[27]	A. A. Azzam, S. A. Shah, A. Catas, L.-I. Cotîrlă, On fuzzy spiral-like functions associated with the family of inear operators, Fractal Fract., 7 (2023), 145. http://doi.org/10.3390/fractalfract7020145 doi: 10.3390/fractalfract7020145
[28]	S. G. Gal, A. I. Ban, Elemente de matematică fuzzy (In Romanian), Romaia: Editura Universităţii din Oradea, 1996.
[29]	S. S. Miller, P. T. Mocanu, Differential subordinations theory and applications, New York, Basel: Marcel Dekker, 2000.
[30]	F. H. Jackson, XI.—On q-functions and a certain difference operator, Trans. Royal Soc. Edin., 46 (1908), 253–281. http://doi.org/10.1017/S0080456800002751 doi: 10.1017/S0080456800002751
[31]	H. Exton, $q$-Hypergeomtric functions and applications, Chichester: Ellis Horwood Limited, 1983.
[32]	U. A. Ezeafulukwe, M. Darus, A note on $q$-calculus, Fasciculi Math., 55 (2015), 53–63. http://doi.org/10.1515/fascmath-2015-0014 doi: 10.1515/fascmath-2015-0014
[33]	M. E. H. Ismail, E. Merkes, D. Styer, A generalization of starlike functions, Complex Var. Elliptic, 14 (1990), 77–84. http://doi.org/10.1080/17476939008814407 doi: 10.1080/17476939008814407
[34]	S. Kanas, R. Raducanu, Some classes of analytic functions related to conic domains, Slovaca, 64 (2014), 1183–1196. http://doi.org/10.2478/s12175-014-0268-9 doi: 10.2478/s12175-014-0268-9
[35]	S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49 (1975), 109–115. http://doi.org/10.2307/2039801 doi: 10.2307/2039801
[36]	S. A. Shah, K. I. Noor, Study on $q$-analogue of certain family of linear operators, Turk. J. Math., 43 (2019), 109–115. http://doi.org/10.3906/mat-1907-41 doi: 10.3906/mat-1907-41
[37]	H. M. Srivastava, A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integr. Transf. Spec. Funct., 18 (2007), 207–216. http://doi.org/10.1080/10652460701208577 doi: 10.1080/10652460701208577
[38]	K. I. Noor, S. Riaz, M. A. Noor, On $q-$Bernardi integral operator, TWMS J. Pure Appl. Math., 8 (2017), 3–11.
[39]	S. A. Shah, L.-I. Cotîrlǎ, A. Catas, C. Dubau, G. Cheregi, A study of spiral-like harmonic functions associated with quantum calculus, J. Funct. Spaces, 22 (2017), 5495011. http://doi.org/10.1155/2022/5495011 doi: 10.1155/2022/5495011
[40]	L.-I. Cotîrlǎ, G. Murugusundaramoorthy, Starlike functions based on Ruscheweyh q-differential operator defined in Janowski domain, Fractal Fract., 7 (2023), 148. http://doi.org/10.3390/fractalfract7020148 doi: 10.3390/fractalfract7020148
[41]	S. M. El-Deeb, L.-I. Cotîrlǎ, Basic properties for certain subclasses of meromorphic p-valent functions with connected q-analogue of linear differential operator, Axioms, 12 (2023), 207. http://doi.org/10.3390/axioms12020207 doi: 10.3390/axioms12020207

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)