Certain Subclasses of Multivalent Functions Defined by New Multiplier Transformations

DENİZ E., ORHAN H.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, vol.36, no.6, pp.1091-1112, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1007/s13369-011-0103-3
  • Journal Name: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1091-1112
  • Keywords: Multiplier transformations, Analytic functions, Multivalent functions, Neighborhoods and partial sums of analytic functions, Fractional calculus operators, FRACTIONAL DERIVATIVE OPERATOR, ANALYTIC-FUNCTIONS, NEGATIVE COEFFICIENTS, BASIC PROPERTIES, VALENT FUNCTIONS, NEIGHBORHOODS, FAMILIES, STARLIKE, CONVEX
  • Ataturk University Affiliated: Yes

Abstract

The new multiplier transformations J(p)(delta)(lambda, mu, l) (delta, l >= 0, lambda >= mu >= 0; p is an element of N) of multivalent functions are defined. Making use of the operator J(p)(delta)(lambda, mu, l), two new subclasses P-lambda,mu,l(delta)(A, B; sigma, p) and (P) over tilde (delta)(lambda,mu,l)(A, B; sigma, p) of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, and partial sums, and some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses P-lambda,mu,l(delta)(A, B; sigma, p) and (P) over tilde (delta)(lambda,mu,l)(A, B; sigma, p) are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.