Zalcman conjecture for a subclass of multivalent functions defined by Sălăgean operator

Abstract In this paper, we introduce a new subclass of analytic and multivalent functions by means of the Sălăgean’s differential operator, and obtain the sharp upper bound of Zalcman functional <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">|</m:mo> <m:mrow> <m:msubsup> <m:mi>a</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mn>2</m:mn> </m:msubsup> <m:mo>-</m:mo> <m:msub> <m:mi>a</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>+</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy="false">|</m:mo> </m:mrow> </m:math> {|a_{p+1}^{2}-a_{p+2}|} for functions belong to this class.