A class of univalent functions involving a differentio-integral operator

• Autorzy: Jain P. K. , Sharma P. , Jain V.
• Języki publikacji: EN

Abstrakty

EN

This paper focuses on a generalized linear operator Im which is a combination of both differential and integral operators. Involving this operator, a class Tsk(...) with respect to k-symmetric points is defined. Results based on coefficient inequalities and bounds for this class are obtained. Various integral representations and some consequent results for TS(...) class are also determined. Further, results on partial sums are discussed.

Słowa kluczowe

EN

analytic function; convex function; convolution; subordination

PL

funkcje analityczne; funkcja wypukła; splot; podporządkowanie

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 2
• Strony: 283--297
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Jain P. K.

• Department of Mathematics, University of Delhi, Delhi 110007, India

autor

Sharma P.

• Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, India

autor

Jain V.

• Department of Mathematics, Maharaja Agrasen College, University of Delhi, Delhi 110093, India

Bibliografia

• [1] M. Acu, S. Owa, Note on a class of starlike functions, RIMS, Kyoto, 2006.
• [2] A. Alb Lupaş, A note on a subclass of analytic functions defined by multiplier transformation, Int. J. Open Prob. Com. Anal. 2(2) (2010).
• [3] F. Al-Oboudi, On univalent functions defined by a generalized Salegean operator, Int. J. Math. Sci. 27 (2004), 1429–1436.
• [4] A. A. Amer, M. Darus, On some properties for new generalized derivative operator, Jordan J. Math. Stat. (JJMS) 4(2) (2011), 91–101.
• [5] A. Cătuş, On certain class of p-valent functions defined by new multiplier transformations, Proceedings Book of the International Symposium on Geometric Function Theory and Applications, August 20–24, 2007, TC Istanbul Kultur University, Turkey, 241–250.
• [6] N. E. Cho, T. H. Kim, Multiplier transformations and strongly close-to-close functions, Bull. Korean Math. Soc. 40(3) (2003), 399–410.
• [7] N. E. Cho, H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37(1–2) (2003), 39–49.
• [8] T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746–765.
• [9] V. P. Gupta, P. K. Jain, Certain classes of univalent functions with negative coefficients, Bull. Austral. Math. Soc. 14 (1976), 409–416.
• [10] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115.
• [11] G. S. Sălăgean, Subclasses of univalent functions, Lecture Notes in Math. (Springer-Verlag), 1013 (1983), 362–372.
• [12] K. Al-Shaqsi, M. Darus, On univalent functions with respect to k-summetric points defined by a generalization Ruscheweyh derivative operators, J. Anal. Appl. 7(1) (2009), 53–61.
• [13] K. Al-Shaqsi, M. Darus, An operator defined by convolution involving the polylogarithms functions, J. Math. & Stat. 4(1) (2008), 46–50.
• [14] K. Al-Shaqsi, M. Darus, A multiplier transformation defined by convolution involving nth order polylogarithms functions, International Mathematical Forum 4 (2009), 1823–1837.
• [15] K. Al-Shaqsi, M. Darus, Differential subordination with generalized derivative operator, AJMMS (to appear).
• [16] H. Silverman, A survey with open problems on univalent functions whose coefficients are negative, Rocky Mountain J. Math. 21(3) (1991), 1099–1125.
• [17] B. A. Uralegaddi, C. Somanatha, Certain classes of univalent functions, Current topics in analytic function theory, World. Sci. Publishing, River Edge, N.Y., (1992), 371–374.