Majorization Results Based upon the Bernardi Integral Operator
نویسندگان
چکیده
By making use of some families integral and derivative operators, many distinct subclasses analytic, starlike functions, symmetric functions have already been defined investigated from numerous perspectives. In this article, with the help one-parameter Bernardi operator, we investigate several majorization results for class normalized which are associated Janowski functions. We also give particular cases our main results. Finally, direct interested readers to possibility examining fundamental or quantum (or q-) extensions findings provided in work concluding section. However, (p,q)-variations suggested q-results will provide relatively minor inconsequential developments because additional (rather forced-in) parameter p is obviously redundant.
منابع مشابه
Integral majorization Polytopes
Let n be a positive integer. We may write (or split) n as sums of n nonincreasing nonnegative integers p1, p2, . . . , pn in different ways (or partitions; see Section 2). For example, 3 = 3 + 0 + 0 = 2 + 1 + 0 = 1 + 1 + 1. If we denote by P (n) the number of different partitions of n, then P (3) = 3. One may check that P (5) = 7. As n gets large, P (n) increases rapidly. It is astounding that ...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2022
ISSN: ['0865-4824', '2226-1877']
DOI: https://doi.org/10.3390/sym14071404