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Some properties of certain subclasses of analytic functions with negative coefficients by using generalized Ruscheweyh derivative operator

Erhan DenizHalit Orhan — 2010

Czechoslovak Mathematical Journal

By making use of the known concept of neighborhoods of analytic functions we prove several inclusions associated with the ( j , δ ) -neighborhoods of various subclasses of starlike and convex functions of complex order b which are defined by the generalized Ruscheweyh derivative operator. Further, partial sums and integral means inequalities for these function classes are studied. Relevant connections with some other recent investigations are also pointed out.

Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points

Nihat YagmurHalit Orhan — 2014

Mathematica Bohemica

The authors obtain the Fekete-Szegő inequality (according to parameters s and t in the region s 2 + s t + t 2 < 3 , s t and s + t 2 , or in the region s 2 + s t + t 2 > 3 , s t and s + t 2 ) for certain normalized analytic functions f ( z ) belonging to k -UST λ , μ n ( s , t , γ ) which satisfy the condition ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) > k ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) - 1 + γ , z 𝒰 . Also certain applications of the main result a class of functions defined by the Hadamard product (or convolution) are given. As a special case of this result, the Fekete-Szegő inequality for a class of functions defined through fractional derivatives is obtained....

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