"The object of the present paper is to obtain several fuzzy differential subordinations associated with Linear operator $$\mathcal{D}_{n,\delta ,g}^{m}f(z) =z+\sum\limits_{j=2}^{\infty }\left[ 1+\left( j-1\right) c^{n}(\delta )\right] ^{m}a_{j}b_{j}z^{j}.$$ Using $\mathcal{D}_{n,\delta ,g}^{m},$ we also introduce a class $\mathcal{H}_{n,m,\delta }^{F}\left( \eta ,g\right) $ univalent analytic f...

In this article, we introduce and study two new families of analytic functions by using strong differential subordinations superordinations associated with Wanas operator/. We also give establish some important properties these families.

In this paper, we consider some relations related to the representations of starlike and convex functions, obtain sufficient conditions for functions by using theory differential subordination. Actually, generalize a result Suffridge analytic with missing coefficients then apply that generalization obtaining different methods implications or functions. Our results improve previous in literature.

The paper is a review of the latest results I. R. Kayumov and S. Ponnusamy on Bohr inequality. An exact estimate in strong inequality obtained Bohr–Rogosinski radius for certain class subordinations examined. All are exact.

The aim of the present paper is to study the p-valent analytic functions in the unit disk and satisfy the differential subordinations z Ip r, λ f z j 1 / p − j Ip r, λ f z j ≺ a aB A − B β z /a 1 Bz , where Ip r, λ is an operator defined by Sălăgean and β is a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting pr...