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Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated. 1. Introduction. Let A denote the class of functions of the form f (z) = z+ ∞ n=2 a n z

Ruscheweyh'and She&Small proved the P6lya-Schoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that clos&o-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form… (More)

By applying certain integral operators to p-valent functions we define a comprehensive family of analytic functins. The subordinations properties of this family is studied, which in certain special cases yield some of the previously obtained results.

We determine conditions under which the partial sums of the Libera integral operator of functions of bounded turning are also of bounded turning.

Inequalities involving multipliers using the sequences {c n } and {d n } of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {c n } and {d n }, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many… (More)

We establish the existence and uniqueness of an attractive fractional coupled system. Such a system has applications in biological populations of cells. We confirm that the fractional system under consideration admits a global solution in the Sobolev space. The solution is shown to be unique. The technique is founded on analytic method of the fixed point… (More)

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its… (More)