Some inequalities involving differential operators and their applications to certain multivalent functions

• Autorzy: Dziok J. , Huseyin I. , Piejko K.
• Języki publikacji: EN

Abstrakty

EN

The main object of the present paper is to investigate several results of certain differential operators which were recently introduced and (or) studied in a series of papers by Chen et et al. [1-3], Irmak et al. [8, 10, 11], Dziok et al. [5, 6] and Liu et al. [14]. In addition, some applications of our results involving certain differential inequalities of multivalently analytic and (or) multivalently raeromorphic functions are given. Our certain results also include some recent results in [5, 6, 9, 11, 12].

Słowa kluczowe

EN

Jack's lemma; analytic functions; multiwalent functions; meromorphic functions; convex functions; starlike functions; differential operators; inequalities

PL

funkcja analityczna; funkcja wielolistna; funkcja wielowartościowa; funkcja meromorficzna; funkcja wypukła; funkcja gwiaździsta; operator różniczkowy; nierówność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2007
• Tom: Vol. 29
• Strony: 109--120
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Dziok J.

autor

Huseyin I.

autor

Piejko K.

• Institute of Mathematics University of Rzeszów ul. Rejtana 16 A, PL-35-310 Rzeszów, Poland

Bibliografia

• [1] M. P. Chen, H. Irmak and H. M. Srivastava, Some families of multivalently analytic functions with negative coefficients, J. Math. Anal. Appl. 214(4)(1997), 674-690.
• [2] M. P. Chen, H. Irmak and H. M. Srivastava, Some multivalent functions with negative coefficients defined by using a differential operators, PanAmer. Math. J. 6(2)(1996), 55-64.
• [3] M. P. Chen, H. Irmak, H. M. Srivastava and C. S. Yu, Some subclasses meromorphically multivalent functions with negative or positive coefficients, PanAmer. Math. J. 7(4)(1997), 53-72.
• [4] P. L. Duren, Univalent Functions, Grundlehren der Mathematishen Wissenschaften 259, Springer-Yerlag, 1983.
• [5] J. Dziok and H. Irmak, Certain classes and inequalities and their applications to multivalent functions, Folia Sci. Univ. Tech. Resov. 25(2001), 55-62.
• [6] J. Dziok and H. Irmak, Certain operators and inegualities and their applications to meromorphically multivalent functions, Demonstratio Math. 36(4)(2003), 839-846.
• [7] A. W. Goodman, Univalent Functions. Vols. I and II, Polygonal Publishing Company, 1983.
• [8] H. Irmak, N. E. Cho and S. H. Lee, Some multivalently starlike functions with negative coefficients and their subclasses defined by using a differential operator, Kyungpook Math. J. 37(1)(1997), 43-51.
• [9] H. Irmak and S. Owa, Certain inegualities for multwalent starlike and meromorphically multivalent starlike functions, Buli. Inst. Math. Acad. Sinica 31(1)(2003), 11-21.
• [10] H. Irmak and Ö. F. Çetin, Some theorems involving inegualities on p-valent functions, Turkish J. Math. 23(1999), 453-459.
• [11] H. Irmak, N. E. Cho, Ö. F. Çetin and R. K. Raina, Certain inegualities involving meromorphically multivalent functions, Hacet. Bull. Nat. Sci. Eng. Ser. B 30(2001), 39-43.
• [12] H. Irmak and R. K. Raina, The starlikeness and convexity of multivalent functions involving certain inequalities, Rev. Math. Comput. 16(2)(2003), 391-398.
• [13] I. S. Jack, Functions starlike and convex of order ?, J. London Math. Soc. 3(1971), 469-474.
• [14] J. L. Liu and H. M. Srivastava, A lineer operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl. 259(2001), 566-581.
• [15] H. M. Srivastava and S. Owa (Editors), Current Topics in Analytic Functions Theory, World Scientific Publ. Comp., 1992.