Fuzzy differential subordinations connected with convolution

Abstract

"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 the operator $\mathcal{D}_{n,\delta ,g}^{m},$ we also introduce a class $\mathcal{H}_{n,m,\delta }^{F}\left( \eta ,g\right) $ of univalent analytic functions for which we give some properties."

New Results about Fuzzy Differential Subordinations Associated with Pascal Distribution

“…We define the fuzzy differential subordination general theory and its applications (see [9][10][11][12][13]). The method of fuzzy differential subordination is applied in the next section to obtain a set of fuzzy differential subordinations related to the operator N r,m q,λ .…”

Fuzzy Differential Inequalities for Convolution Product of Ruscheweyh Derivative and Multiplier Transformation

“…The dual notion, namely fuzzy differential superordination, was introduced in 2017 [14]. Since then, numerous researchers have studied different properties of differential operators involving fuzzy differential subordinations and superordinations: Wanas operator [15,16], generalized Noor-Sȃlȃgean operator [17], Ruscheweyh and Sȃlȃgean operators [18] or a linear operator [19]. Univalence criteria were also derived using fuzzy differential subordination theory [20].…”

Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator

“…At the beginning of 2012, a new research direction was launched by combining the concept of differential subordination with the complex function domain in fuzzy set theory, which is named fuzzy differential subordination. For more details, see [5,6,[13][14][15][16][17][18][19]. These articles go further into the subject of fuzzy differential subordination and how it applies to different operators.…”