In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator and the differential subordination principle. Inclusion relationships for these subclasses are established. Moreover, we introduce some integral-preserving properties. Key-Words: Starlike function; Convex function; ...

The subordination of clauses, and the recursion which results, lies at the heart of linguistic representation. Yet there are many aspects of subordination that are not fully understood. An enduring puzzle is that some clauses which appear to be structurally subordinate nevertheless pattern with main clauses in certain, but not all, respects. This paper posits that such clauses, which we term “q...

In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.

Recently the present authors established refined versions of Bohr's inequality in case bounded analytic functions. In this article, we state and prove a generalization these results. Here, consider image origin boundary unit disk under function question let distance between both play central role our theorems. Thereby extend Bohr for class quasi-subordinations which contains classes majorizatio...

The object of the present paper is to introduce and investigate new subclasses of the function class Σ of bi-univalent functions defined in the open unit disk U, involving quasi subordination. The coefficients estimate |a2| and |a3| for functions in these new subclasses are also obtained. c ©2017 All rights reserved.

We give a proof of L-bounds for the quasi-geostrophic equation and other non-local equations. The proof uses mainly tools from functional analysis, notably the product formulas (also known as “operator splitting methods”) and the Bochner-Pollard subordination identities, hence it could be applicable to other equations. 2010 Mathematics Subject Classification: 47D06, 47F05, 35S10, 35Q99.