The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, part dealing geometric function theory. Several differential subordinations are established regarding operator L?m, given by L?m:An?An, L?mf(z)=(1??)Rmf(z)+?Smf(z), where An={f?H(U),f(z)=z+an+1zn+1+…,z?U} is subclass normalized holomorphic functions and operators Rmf(z) ...

In the present investigation, we obtain certain sufficient conditions for a normalized analytic function f(z) defined by the Dziok–Srivastava linear operator Hm1⁄2a1 to satisfy the certain subordination. Our results extend corresponding previously known results on starlikeness, convexity, and close to convexity. 2006 Elsevier Inc. All rights reserved.

A system for transformation, correlation, and unification of subordinations between d002 (Å) semi-graphite graphite, graphitization degrees metamorphic temperature was created. The existing equations in the literature were analyzed new equations, which determine correlation relationships these parameters, formulated. effect factors that control processes (temperature, general pressure tectonic ...

We address a conjecture of D. Applebaum on small time trace asymptotics for subordinate Brownian motion on compact manifolds. In [1], heat trace asymptotics are computed for the semigroup of the square root of the Laplacian (the generator of the Cauchy process) on the n-dimensional torus, SU(2) and SO(3), and a conjecture is made [1, pp. 2493-2494] that such asymptotics should hold for all α-st...

The notion of strong differential subordination was introduced in 1994 and the theory related to it developed 2009. dual superordination also In a paper published 2012, given new approach by defining classes analytic functions on U×U¯ having as coefficients holomorphic U¯. Using those classes, extended S?l?gean Ruscheweyh operators were operator defined L?m:An?*?An?*,L?mf(z,?)=(1??)Rmf(z,?)+?Sm...

and Applied Analysis 3 Corresponding to a function hp α1, . . . , αq; β1, . . . , βs; z defined by hp ( α1, . . . , αq; β1, . . . , βs; z ) z−pqFs ( α1, . . . , αq; β1, . . . , βs; z ) , 1.11 we now consider a linear operator Hp ( α1, . . . , αq; β1, . . . , βs ) : Σ ( p ) −→ Σp, 1.12 defined by means of the Hadamard product or convolution as follows: Hp ( α1, . . . , αq; β1, . . . , βs ) f z :...

In the present investigation, we obtain some subordination and superordination results involving Hadamard product for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in this paper, with various other known results also pointed out.

In this paper, we discuss and introduce a new study using an integral operator wk,μm in geometric function theory, especially sandwich theorems. We obtained some conclusions for differential subordination superordination formula generalized operator. addition, certain theorems were found. The theory’s features outcomes are symmetric to those derived the theory.