Search

Abstract: Let be the class of all analytic functions f in the open unit disk of the form . For and , two subclasses and of are introduced. In this paper, we find suitable conditions on , c and such that for each satisfying for all , the functionbelongs to or . Here denotes the usual class of starlike of order in . We also determine necessary conditions so that implies thatwhere will be specified. [Copyright &y& Elsevier]

Abstract: Let be the class of functions which are meromorphic in the punctured open unit disk . Applying the results by Nunokawa [M. Nunokawa, On properties of non-Carathéodory functions, Proc. Japan Acad. 68 (1992) 152–153] and Fukui and Sakaguchi [S. Fukui and K. Sakaguchi, An extension of a theorem of S. Ruscheweyh, Bull. Fac. Edu. Wakayama Univ. Nat. Sci. 29 (1980) 1–3], we derive some sufficient conditions for meromorphic strongly starlikeness for function with some interesting corollaries. [Copyright &y& Elsevier]

Abstract: Recently, by applying the principle of subordination for analytic functions in the open unit disk , Kim and Cho [I. H. Kim, N. E. Cho, Sufficient conditions for Carathéodory functions, Comput. Math. Appl. 59 (2010), 2067–2073] considered several sufficient conditions for a family of Carathéodory functions. The main purpose of this paper is to investigate some (presumably new) sufficient conditions for the class of strongly Carathéodory functions in . One illustrative example and several corollaries of the main results presented here are also considered. [Copyright &y& Elsevier]

Abstract: Let be the class of functions with and in the open unit disk . For , is said to be in the class if it satisfies for some complex numbers , and , and for some real . Some interesting properties for associated with close-to-convex functions and starlike functions of order are discussed. [Copyright &y& Elsevier]

Abstract: Let be the class of analytic functions in the open unit disc with and for some real . The object of the present paper is to discuss some properties of in the class . Furthermore, an example for our results is shown. [Copyright &y& Elsevier]

Abstract: For analytic functions normalized with and in the open unit disk , a new class of satisfying some conditions with some complex numbers and is introduced. The object of the present paper is to discuss some properties for of associated with close-to-convex and starlike of order in . [Copyright &y& Elsevier]

Abstract: For analytic functions in the open unit disk and convex functions in , Ch. Pommerenke [Ch. Pommerenke, On close-to-convex analytic functions, Trans. Amer. Math. Soc. 114 (1) (1965) 176–186] has proved one theorem which is a generalization of the result by K. Sakaguchi [K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959) 72–75]. The object of the present paper is to generalize the theorem due to Pommerenke. [Copyright &y& Elsevier]

Abstract: Integral means inequalities with coefficients inequalities of certain analytic functions for the fractional derivatives and the fractional integral are determined by means of the subordination theorem. Relevant connections with known integral means with coefficients inequalities of analytic functions are also pointed out. [Copyright &y& Elsevier]

Abstract: Two subclasses and are introduced concerning with Sakaguchi functions in the open unit disk . Further, by using the coefficient inequalities for the classes and , two subclasses and are defined. The object of the present paper is to discuss some properties of functions belonging to the classes and . [Copyright &y& Elsevier]

Abstract: Applying the coefficient inequalities of functions f(z) belonging to the subclasses of certain analytic functions in the open unit disk , two subclasses are introduced. The object of the present paper is to derive some convolution properties of functions f(z) in the classes . [Copyright &y& Elsevier]

Abstract: Maximum principles for analytic functions are very important tools in the analytic function theory. In the present paper, we consider a maximum principle for a class of non-analytic function defined on the open unit disk. Some examples for our theorems are also shown. [Copyright &y& Elsevier]

Abstract: By using the method of differential subordinations, we derive certain sufficient conditions for Carathéodory functions. Our results extend and improve some results due to [1–4]. [Copyright &y& Elsevier]

Abstract: For analytic functions in the open unit disk , there are many sufficient conditions for to be starlike and convex in . In view of the paper by P.T. Mocanu [P.T. Mocanu, Some starlikeness conditions for analytic functions, Rev. Roumaine Math. Pures Appl. 33 (1988) 117–124], some extensions of sufficient conditions for to be starlike of order and to be convex of order are discussed. [Copyright &y& Elsevier]

Abstract: In the present work, the authors determine coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy–Euler differential equations. Several corollaries and consequences of the main results are also considered. [Copyright &y& Elsevier]

Abstract: The purpose of the present paper is to investigate several subordination- and superordination-preserving properties of a certain class of integral operators, which are defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function. [Copyright &y& Elsevier]

Abstract: Let be the class of functions which are analytic with and in the open unit disk . For such functions , the subclass of is introduced. The object of the present paper is to discuss some properties for in the class concerned with some sufficient conditions for to be univalent in . [Copyright &y& Elsevier]

Abstract: The purpose of the present paper is to derive some differential inequalities for certain analytic functions in the open unit disk by appealing to a result obtained by the first author. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [Copyright &y& Elsevier]