Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator
This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/20/2539 |
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| author | Georgia Irina Oros |
| author_facet | Georgia Irina Oros |
| author_sort | Georgia Irina Oros |
| collection | DOAJ |
| description | This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results. |
| first_indexed | 2024-03-10T06:24:43Z |
| format | Article |
| id | doaj.art-23ad81e326064366945b0e9d8dbaaae5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:24:43Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-23ad81e326064366945b0e9d8dbaaae52023-11-22T19:01:22ZengMDPI AGMathematics2227-73902021-10-01920253910.3390/math9202539Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral OperatorGeorgia Irina Oros0Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, RomaniaThis paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results.https://www.mdpi.com/2227-7390/9/20/2539analytic functionunivalent functionfuzzy differential subordinationfuzzy best dominantconfluent hypergeometric functionintegral operator |
| spellingShingle | Georgia Irina Oros Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator Mathematics analytic function univalent function fuzzy differential subordination fuzzy best dominant confluent hypergeometric function integral operator |
| title | Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator |
| title_full | Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator |
| title_fullStr | Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator |
| title_full_unstemmed | Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator |
| title_short | Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator |
| title_sort | fuzzy differential subordinations obtained using a hypergeometric integral operator |
| topic | analytic function univalent function fuzzy differential subordination fuzzy best dominant confluent hypergeometric function integral operator |
| url | https://www.mdpi.com/2227-7390/9/20/2539 |
| work_keys_str_mv | AT georgiairinaoros fuzzydifferentialsubordinationsobtainedusingahypergeometricintegraloperator |