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Search Results (4)

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Keywords = Dziok–Srivastava operator

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19 pages, 324 KiB  
Article
New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations
by Alina Alb Lupaş
Symmetry 2023, 15(8), 1544; https://doi.org/10.3390/sym15081544 - 5 Aug 2023
Cited by 2 | Viewed by 1083
Abstract
In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended [...] Read more.
In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator Dz−γHmlα1,β1 that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential subordinations and superordinations concerning the operator Dz−γHmlα1,β1 are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties. Full article
(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))
20 pages, 325 KiB  
Article
Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator
by Alina Alb Lupaş
Mathematics 2023, 11(14), 3129; https://doi.org/10.3390/math11143129 - 15 Jul 2023
Cited by 4 | Viewed by 1844
Abstract
Fuzzy set theory, introduced by Zadeh, gives an adaptable and logical solution to the provocation of introducing, evaluating, and opposing numerous sustainability scenarios. The results described in this article use the fuzzy set concept embedded into the theories of differential subordination and superordination [...] Read more.
Fuzzy set theory, introduced by Zadeh, gives an adaptable and logical solution to the provocation of introducing, evaluating, and opposing numerous sustainability scenarios. The results described in this article use the fuzzy set concept embedded into the theories of differential subordination and superordination from the geometric function theory. In 2011, fuzzy differential subordination was defined as an extension of the classical notion of differential subordination, and in 2017, the dual concept of fuzzy differential superordination appeared. These dual notions are applied in this paper regarding the fractional integral applied to Dziok–Srivastava operator. New fuzzy differential subordinations are proved using known lemmas, and the fuzzy best dominants are established for the obtained fuzzy differential subordinations. Dual results regarding fuzzy differential superordinations are proved for which the fuzzy best subordinates are shown. These are the first results that link the fractional integral applied to Dziok–Srivastava operator to fuzzy theory. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
18 pages, 319 KiB  
Article
Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator
by Ekram Elsayed Ali, Mohamed Kamal Aouf, Rabha Mohamed El-Ashwah and Teodor Bulboacă
Mathematics 2022, 10(17), 3064; https://doi.org/10.3390/math10173064 - 25 Aug 2022
Viewed by 1437
Abstract
In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized [...] Read more.
In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)
8 pages, 218 KiB  
Article
Geometric Properties of Certain Analytic Functions Associated with the Dziok-Srivastava Operator
by Cai-Mei Yan and Jin-Lin Liu
Symmetry 2019, 11(2), 259; https://doi.org/10.3390/sym11020259 - 19 Feb 2019
Cited by 2 | Viewed by 1948
Abstract
The objective of the present paper is to derive certain geometric properties of analytic functions associated with the Dziok–Srivastava operator. Full article
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
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