Multivalent Harmonic Functions defined by m-tuple Integral operators

• Autorzy: Sharma, P.
• Języki publikacji: EN

Słowa kluczowe

EN

Multivalent Harmonic starlike (convex) functions; Erdélyi-Kober integral operator; Hohlov operator; Carlson and Shaffer operator; convolution; Wright's generalized hypergeometric function; Gauss hypergeometric function; incomplete beta function

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 1
• Strony: 87-101
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Sharma, P.

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

Bibliografia

• [1] B.C. Carlson and D.B. Shaffer, Starlike and prestarlike hyprgeometric functions, SIAMJ. Math. Anal. 15 (1984), 737-745.
• [2] E.M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc.(Ser.2) 46 (1940), 389-408.
• [3] H.M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limlted and John Wiley & Sons) New York, Chichester,Toronto.
• [4] H. Bateman, A. Erd´elyi, W. Magnus, F. Oberhettinger, F.G. Ticomi (Eds.), Higher Transcendental Functions, Vol. 1, MaGraw-Hill, New York, 1953.
• [5] J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.
• [6] L.J. Slater, Generalized Hypergeometric functions, Cambridge Univ. Press, London 1966.
• [7] O.P. Ahuja and J.M. Jahangiri, On a linear combination of multivalently harmonic functions, Kyungpook Math. J. 42 (2002), 61-71.
• [8] O.P. Ahuja and J.M. Jahangiri, Multivalent harmonic starlike functions, Ann. Univ. Mariae Curie-Sklodowska, Sectio A, 55(1) (2001), 1-13.
• [9] O.P. Ahuja and J.M. Jahangiri, Errata to Multivalent harmonic starlike function, Ann.Univ.Mariae Curie-Sklodowska, Vol.LV,1 Sectio A 56(1) (2002), 105.
• [10] O.P. Ahuja and J.M. Jahangiri, Multivalent harmonic convex functions, submited for publication.
• [11] O.P. Ahuja and S.B. Joshi and A. Swaminathan, Multivalent Harmonic Convolution Operators Associated With Generalized Hypergeometric Functions, submitted for publication.
• [12] O.P. Ahuja and H. Silverman, Inequalities Associating Hypergeometric functions with Planer Harmonic Mapping, J. Ineq. Pure Appl. Math. 5(4) Art.99, 2004.
• [13] O.P. Ahuja, Harmonic Starlikeness and Convexity of Integral Operators generated by hypergeometric Series, Integral Transforms and Special Functions (2009), 1-13.
• [14] O.P. Ahuja, Interconnectivity of Hohlov-Type Harmonic Convolution Operators with the Harmonic Starlike Mapping, to appear.
• [15] P. Duren, W. Hengartner and R.S. Laugesen, The Argument Principle for Harmonic Functions, Amer. Math. Monthly, 103 (1996), 411-415.
• [16] V.S. Kriyakova, Generalized Fractional Calculas and Applications, Pitman Research Notes in Math. Series, 301, Longman, Harlow (U.K.) 1994.
• [17] V.S. Kriyakova, M. Saigo, S. Owa, Study on differential operator and Integral operators in Univalent Function Theory, Res. Inst. Math. Sci. Kyoto Seminar, March 3-5 (2003), 12-30.
• [18] V.S. Kriyakova, M. Saigo and H.M. Srivastava, Fract. Calc. Appl. Anal. 1, No. 1, 1998, 79-104.
• [19] Yu. F. Hovlov, Convolution operators preserving univalent functions, Pliska Stud. Math. Bulgar. 10 (1989), 87-92.