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Some subclasses of analytic functions involving certain integral operator

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce and investigate two new subclasses of analytic functions with bounded boundary and bounded radius rotations by using a certain p-valent operator which complies with the known Carlson-Shaffer operator for p = 1. Both of these operators are heavily explored and have various applications. We investigate some inclusions results and integral preserving properties. We also extend the Ruscheweyh and Sheil-Small convolution preserving properties in the context of these classes. We relate our finding with the existing known results found in the literature regarding this subject.
Wydawca
Rocznik
Strony
285--293
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250 (AJK), Pakistan
  • Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
Bibliografia
  • [1] M. K. Aouf, On a class of p-valent starlike functions of order α, Internat. J. Math. Math. Sci. 10 (1987), no. 4, 733-744.
  • [2] M. K. Aouf, On a class of p-valent close-to-convex functions of order β and type α, Internat. J. Math. Math. Sci. 11 (1988), no. 2, 259-266.
  • [3] M. K. Aouf, H. M. Hossen and H. M. Srivastava, Some families of multivalent functions, Comput. Math. Appl. 39 (2000), no. 7-8, 39-48.
  • [4] S. Z. H. Bukhari, Some subclasses of analytic functions related with the generalizations of functions with bounded boundary rotation, PhD Thesis, COMSATS Institute of Information Technology, 2012, http://prr.hec.gov.pk/jspui/bitstream/123456789/1564/1/2118S.
  • [5] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), no. 4, 737-745.
  • [6] A. W. Goodman, On the Schwarz-Christoffel transformation and p-valent functions, Trans. Amer. Math. Soc. 68 (1950), 204-223.
  • [7] W. Janowski, Some extremal problems for certain families of analytic functions. I, Ann. Polon. Math. 28 (1973), 297-326.
  • [8] E. Lindelöf, Mémoire sur certaines inégalitis dans la théorie des functions, monogénses et sur quelques propriétés nouvelles de ces fonctions dans levoisinage d’un point singulier essentiel, Ann. Soc. Sci. Fenn. 35 (1909), no. 7, 1-35.
  • [9] A. E. Livingston, p-valent close-to-convex functions, Trans. Amer. Math. Soc. 115 (1965), 161-179.
  • [10] S. S. Miller and P. T. Mocanu, Differential Subordinations. Theory and Applications, Monogr. Textb. Pure Appl. Math. 225, Marcel Dekker, New York, 2000.
  • [11] K. I. Noor, On functions of bounded boundary rotation of complex order, Soochow J. Math. 20 (1994), 101-111.
  • [12] K. I. Noor, On close-to-convex functions of complex order, Soochow J. Math. 26 (2000), no. 4, 369-376.
  • [13] K. I. Noor, On classes of analytic functions defined by convolution with incomplete beta functions, J. Math. Anal. Appl. 307 (2005), no. 1, 339-349.
  • [14] K. I. Noor, On analytic functions related to certain family of integral operators, JIPAM. J. Inequal. Pure Appl. Math. 7 (2006), no. 2, Article ID 69.
  • [15] K. I. Noor, Some properties of analytic functions with bounded radius rotation, Complex Var. Elliptic Equ. 54 (2009), no. 9, 865-877.
  • [16] K. I. Noor and S. Z. Hussain Bukhari, On analytic functions related with generalized Robertson functions, Appl. Math. Comput. 215 (2009), no. 8, 2965-2970.
  • [17] K. I. Noor and D. K. Thomas, Quasiconvex univalent functions, Internat. J. Math. Math. Sci. 3 (1980), no. 2, 255-266.
  • [18] S. Owa, On certain classes of p-valent functions with negative coefficients, Simon Stevin 59 (1985), no. 4, 385-402.
  • [19] K. S. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31 (1975/76), no. 3, 311-323.
  • [20] D. A. Patil and N. K. Thakare, On convex hulls and extreme points of p-valent starlike and convex classes with applications, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N. S.) 27(75) (1983), no. 2, 145-160.
  • [21] B. Pinchuk, Functions of bounded boundary rotation, Israel J. Math. 10 (1971), 6-16.
  • [22] Y. Polatoglu, M. Bolcal, A. Şen and E. Yavuz, A study on the generalization of Janowski functions in the unit disc, Acta Math. Acad. Paedagog. Nyházi. (N. S.) 22 (2006), no. 1, 27-31.
  • [23] G. Pólya and I. J. Schoenberg, Remarks on de la Vallée Poussin means and convex conformal maps of the circle, Pacific J. Math. 8 (1958), 295-334.
  • [24] M. O. Reade, The coefficients of close-to-convex functions, Duke Math. J. 23 (1956), 459-462.
  • [25] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.
  • [26] S. Ruscheweyh, Convolutions in Geometric Function Theory, Université de Montréal, Montreal, 1982.
  • [27] S. Ruscheweyh and T. Sheil-Small, Hadamard products of Schlicht functions and the Pólya-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135.
  • [28] H. Saitoh, A linear operator and its applications of first order differential subordinations, Math. Japon. 44 (1996), no. 1, 31-38.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c60988b2-ede6-42bd-b45b-a4312fee2887
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