Strong differential sandwich results of l-pseudo-starlike functions with respect to symmetrical points

Abstract

In the present investigation, by considering suitable classes of admissible functions, we establish strong differential subordination and superordination properties for λ-pseudo-starlike functions with respect to symmetrical points in the open unit disk U . These results are applied to obtain strong differential sandwich results.2010 Mathematics Subject Classification. Primary: 30C45; Secondary: 30A20.

Results of Third-Order Strong Differential Subordinations

“…There have been many interesting and fruitful usages of a wide variety of first-order and second-order strong differential subordinations for analytic functions. Recently, many researchers have worked in this direction and proved several significant results that can be seen in [6][7][8]. Various strong differential subordinations were established by linking different types of operators to the study.…”

Some applications of first-order differential subordinations for holomorphic functions in complex normed spaces

“…The existing literature in Geometric Function Theory of Complex Analysis contains a considerably large number of interesting investigations dealing with differential subordination problems for analytic functions in the unit disk U (see, for example, [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16][17][18]). In particular, in the recently-published survey-cum-expository review article by Srivastava [7], the so-called (p, q)-calculus was exposed to be a rather trivial and inconsequential variation of the classical q-calculus, the additional parameter p being redundant or superfluous (see, for details, [7, p. 340]).…”

Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

“…). We denote by Q * the set of functions that are analytic and injective on U × Results involving strong differential superordination investigated with operators began to be published shortly after the concept was introduced [9], continued to demonstrate the topic's interest in the following years ( [10,11]) and are still in development, as evidenced by the numerous papers published in recent years ( [12][13][14][15][16][17]). The differential operator studied in [18] was extended in the paper published in 2012 [19] to the new class of analytic functions A * nζ using the definitions given below.…”