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Properties of analytic functions defined by an integral operator

100%

Cotîrlă L. I.

2010

tom Vol. 43, nr 4

799-803

In this paper we present some properties for the analytic functions in the open unit disc U defined by an integral operator.

New criteria for univalence of certain integral operators

100%

Pescar V.

tom Vol. 33, nr 1

51-54

On certain general integral operators of analytic functions

100%

Frasin B. A.

tom 66

nr 1

In this paper, we obtain new sufficient conditions for the operators \(F_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) and \(G_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) to be univalent in the open unit disc \(\mathcal{U}\), where the functions \(f_1, f_2,..., f_n\) belong to the classes \(S^*(a, b)\) and \(\mathcal{K}(a, b)\). The order of convexity for the operators \(F_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) and \(G_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) is also determined. Furthermore, and for \(\beta= 1\), we obtain sufficient conditions for the operators \(F_n(z)\) and \(G_n(z)\) to be in the class \(\mathcal{K}(a, b)\). Several corollaries and consequences of the main results are also considered.

Generating relations involving hypergeometric functions by means of integral operators

100%

Pathan M. , Khan S.

2002

tom Vol. 35, nr 1

35-39

In this paper, the focus is on the results which involve exponential functions. The results of Pathan and Yasmeen [6] and Exton [3] are used with a view to obtaining generating functions which are partly unilateral and partly bilateral.

Applications of convolution properties

44%

Trojnar-Spelina L.

tom Vol. 46, nr 3

513--523

K. I. Noor (2007 Appl. Math. Comput. 188, 814–823) has defined the classes Qk(a, b, λ, γ) and Tk(a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes.