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Successive coefficients for spirallike and related functions

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2019年第4期113卷 2969-2979页

作者： Arora, Vibhuti Ponnusamy, Saminathan Sahoo, Swadesh Kumar Indian Inst Technol Indore Discipline Math Khandwa Rd Indore 453552 Madhya Pradesh India Indian Inst Technol Madras Dept Math Chennai 600036 Tamil Nadu India

We consider the family of all analytic and univalent functions in the unit disk of the form f (z) = z + a2z2 + a3z3 + center dot center dot center dot. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is vertical bar an+ 1 vertical bar - vertical bar an vertical bar , for f belonging to the family of. - spirallike functions of order a. Our particular results include the case of starlike and convex functions of order a and other related class of functions.

关键词： convex functions close-to-convex functions Starlike functions Spirallike functions Successive coefficients

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On a class of analytic functions with missing coefficients

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APPLIED MATHEMATICS AND COMPUTATION 2010年第9期215卷 3473-3481页

作者： Yang, Ding-Gong Liu, Jin-Lin Yangzhou Univ Dept Math Yangzhou 225002 Jiangsu Peoples R China Suzhou Univ Dept Math Suzhou 215006 Jiangsu Peoples R China

Let T-n(A, B, alpha) denote the class of functions of the form: f(z) = z + Sigma(infinity)(k=n+1) a(k)z(k) (n is an element of N = {1, 2, 3, ... }), which are analytic in the open unit disk U and satisfy the following subordination condition: f'(z) + alpha zf ''(z) < 1 + Az/1 + Bz (z is an element of U;-1 <= B < 1;B < A;alpha > 0). In this paper, we find the sharp lower bound on |z| = r < 1 for the functional Re{f'(z) + alpha zf ''(z)} over the class: T-n(A, B, 0) = { f(z) = z + Sigma(infinity)(k=n+1) a(k)z(k) f'(z) < 1 + Az/1 + Bz (n is an element of N = {1, 2, 3, ... };z is an element of U)}. By applying this result, several interesting consequences are given. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Analytic functions Univalent functions convex functions close-to-convex functions Subordination Sharp bounds

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Argument inequalities for certain analytic functions

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MATHEMATICAL AND COMPUTER MODELLING 2010年第9-10期52卷 1812-1821页

作者： Yang, Ding-Gong Liu, Jin-Lin Yangzhou Univ Dept Math Yangzhou 225002 Jiangsu Peoples R China Suzhou Univ Dept Math Suzhou 215006 Jiangsu Peoples R China

Let q be analytic in the open unit disk U with q(0) = 1 and q(z) not equal 0 (z is an element of U). By using the method of differential subordinations, we derive certain conditions involving q and zq' under which the functions q satisfy the following two-sided inequality: alpha(2)pi/2 < argq(z) alpha(1)pi/2 (z is an element of U) for some alpha(1) and alpha(2) (0 < alpha(1), alpha(2) <= 1). Several interesting consequences of the main results are also given. All these results presented here are sharp. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Analytic functions Multivalent functions Starlike functions Strongly starlike functions close-to-convex functions Subordination

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A certain subclass of analytic functions involving operators of fractional calculus

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1998年第5期35卷 83-91页

作者： Chen, MP Irmak, H Srivastava, HM Acad Sinica Inst Math Taipei 11529 Taiwan Kirikkale Univ Fac Sci & Letters Dept Math TR-71450 Yahsihan Turkey Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada Tamkang Univ Tamsui 25137 Taiwan Soochow Univ Taipei 11102 Taiwan Natl Tsing Hua Univ Hsinchu Taiwan Chung Yuan Christian Univ Chungli Taiwan

Making use of certain operators of fractional calculus, we introduce a new class T-mu(n,lambda,alpha) of functions which are analytic and univalent in the open unit disk U and obtain a necessary and sufficient condition for a function to be in the class T-mu(n,lambda,alpha). The various other results presented here for the class T-mu(n,lambda,alpha) include the radii of close-to-convexity, starlikeness, and convexity, end some growth and distortion theorems involving fractional integrals and fractional derivatives. Some interesting consequences and possible further generalizations of these results are also pointed out.

关键词： analytic functions univalent functions fractional calculus (fractional integral and fractional derivative) close-to-convex functions starlike functions convex functions maximum modulus theorem growth and distortion theorems Gauss hypergeometric function

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On some length problems for univalent functions

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2016年第7期39卷 1662-1666页

作者： Nunokawa, Mamoru Sokol, Janusz Gunma Univ Chuou Ward Hoshikuki Cho 798-8 Chiba 2600808 Japan Rzeszow Univ Technol Dept Math Al PowstancowWarszawy 12 PL-35959 Rzeszow Poland

Let A be the class of functions f(z) = z + Sigma(infinity)(n=2) a(n)z(n), which are analytic in the unit disk D = {z : vertical bar z vertical bar 1. Later, in 1969 Nunokawa has shown that if f is convex univalent, t... 详细信息

Let A be the class of functions f(z) = z + Sigma(infinity)(n=2) a(n)z(n), which are analytic in the unit disk D = {z : vertical bar z vertical bar < 1}. Let C(r) be the closed curve that is the image of the circle vertical bar z vertical bar = r < 1 under the mapping w = f(z), L(r) the length of C(r), and let A(r) be the area enclosed by the curve C(r). In 1968 D.K. Thomas shown that if f 2 A, f is starlike with respect to the origin, and for 0 <= r < 1, A(r) < A, an absolute constant, then L(r) = O (log 1/1 - r) as r -> 1. Later, in 1969 Nunokawa has shown that if f is convex univalent, then L(r) = O {A(r) log 1/1 - r}(1/2) as r -> 1. This paper is devoted to obtaining a related correspondence between f(z) and L(r) for the case when f is univalent. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： close-to-convex functions convex functions starlike functions length problem

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Some functional inequalities and inclusion relationships associated with certain families of integral operators

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2005年第11-12期49卷 1787-1795页

作者： Gao, CY Yuan, SM Srivastava, HM Changsha Univ Sci & Technol Dept Math & Comp Sci Changsha 410076 Hunan Peoples R China Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada

By making use of certain familiar integral operators, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex functions. Among other results presented here, the authors establish a number of inclusion relationships associated with some of these integral operators. Some of the results established in this paper would provide extensions of those given in earlier works. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： analytic functions univalent functions starlike functions convex functions close-to-convex functions quasi-convex functions Jung-Kim-Srivastava operators Bernardi operator Miller-Mocanu lemma multiplier transformation fractional integral factional derivative

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Properties for uniformly starlike and related functions under the Srivastava-Attiya operator

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APPLIED MATHEMATICS AND COMPUTATION 2011年第7期218卷 3615-3623页

作者： Sun, Yong Kuang, Wei-Ping Wang, Zhi-Gang Huaihua Univ Dept Math Huaihua 418008 Hunan Peoples R China Anyang Normal Univ Sch Math & Stat Anyang 455002 Hunan Peoples R China

In the present paper, we introduce and investigate classes of analytic functions involving the Srivastava-Attiya operator. Basic properties for beta-uniformly starlike functions of order gamma are studied, such as inclusion relations, sufficient conditions, coefficient inequalities and distortion inequalities. The results are also extended to beta-uniformly convex, close-to-convex, and quasi-convex functions. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Uniformly starlike functions convex functions close-to-convex functions Quasi-convex functions Inclusion relations Coefficient inequalities Srivastava-Attiya operator

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Geometric properties of solutions of a class of ordinary linear differential equations

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期187卷 408-416页

作者： Saltoh, Hitoshi Gunma Natl Coll Technol Dept Math Gunma 3718530 Japan

The main object of this paper is to investigate several geometric properties of the solutions of the following second-order linear differential equation: w"(z) +p(z)w(z) = 0, where the function p(z) is analytic in the open unit disk U. Relevant connections of the results presented in this paper with those given earlier by, for example, Robertson, Miller and Saitoh are also considered. (C) 2006 Published by Elsevier Inc.

关键词： starlike functions strongly starlike functions close-to-convex functions differential equations univalent function

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On certain sufficient conditions for close-to-convexity

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期187卷 369-378页

作者： Patel, J. Cho, N. E. Utkal Univ Dept Math Bhubaneswar 751004 Orissa India Pukyong Natl Univ Dept Appl Math Pusan 608737 South Korea

In this paper, we derive certain sufficient conditions for close-to-convexity of analytic functions by using the techniques of differential subordinations. Relevant connections of the results presented here with those... 详细信息

关键词： analytic functions p-valent functions hypergeometric function close-to-convex functions subordination between analytic functions

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Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010年第4期59卷 1578-1583页

作者： Swaminathan, A. Indian Inst Technol Dept Math Roorkee 247667 Uttarkhand India

The author aims at finding certain conditions on the parameters a, b and c such that the normalized Gaussian hypergeometric function zF(a, b;c;z) given by F (a, b;c;z) = Sigma(infinity)(n=0) (a)(n)(b)(n)/(c)(n)(1)(n) z(n), vertical bar z vertical bar < 1, is in a certain class of analytic functions. Various results for the particular values of these parameters are deduced. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Univalent convex Starlike close-to-convex functions Gaussian hypergeometric functions Incomplete beta functions

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