Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator
This article presents certain families of analytic functions regarding <i>q</i>-starlikeness and <i>q</i>-convexity of complex order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>γ</mi> <mspace width=...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-05-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/11/5/719 |
| _version_ | 1811186490072367104 |
|---|---|
| author | Shahid Mahmood Nusrat Raza Eman S. A. AbuJarad Gautam Srivastava H. M. Srivastava Sarfraz Nawaz Malik |
| author_facet | Shahid Mahmood Nusrat Raza Eman S. A. AbuJarad Gautam Srivastava H. M. Srivastava Sarfraz Nawaz Malik |
| author_sort | Shahid Mahmood |
| collection | DOAJ |
| description | This article presents certain families of analytic functions regarding <i>q</i>-starlikeness and <i>q</i>-convexity of complex order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>γ</mi> <mspace width="4pt"></mspace> <mo>(</mo> <mi>γ</mi> <mo>∈</mo> <mi mathvariant="double-struck">C</mi> <mo>\</mo> <mfenced open="{" close="}"> <mn>0</mn> </mfenced> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. This introduced a <i>q</i>-integral operator and certain subclasses of the newly introduced classes are defined by using this <i>q</i>-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>δ</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo></mrow></semantics></math></inline-formula>-neighborhood of analytic functions are introduced and the inclusion relations between the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>δ</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo></mrow></semantics></math></inline-formula>-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed. |
| first_indexed | 2024-04-11T13:46:17Z |
| format | Article |
| id | doaj.art-842dd5d1e17d4cc2abfa3041fba3d298 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:46:17Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-842dd5d1e17d4cc2abfa3041fba3d2982022-12-22T04:21:03ZengMDPI AGSymmetry2073-89942019-05-0111571910.3390/sym11050719sym11050719Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral OperatorShahid Mahmood0Nusrat Raza1Eman S. A. AbuJarad2Gautam Srivastava3H. M. Srivastava4Sarfraz Nawaz Malik5Department of Mechanical Engineering, Sarhad University of Science & Information Technology, Ring Road, Peshawar 25000, PakistanMathematics Section, Women’s College, Aligarh Muslim University, Aligarh 202001, Uttar Pradesh, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202001, Uttar Pradesh, IndiaDepartment of Mathematics and Computer Science, Brandon University, 270 18th Street, Brandon, MB R7A 6A9, CanadaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, COMSATS University Islamabad, Wah Campus 47040, PakistanThis article presents certain families of analytic functions regarding <i>q</i>-starlikeness and <i>q</i>-convexity of complex order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>γ</mi> <mspace width="4pt"></mspace> <mo>(</mo> <mi>γ</mi> <mo>∈</mo> <mi mathvariant="double-struck">C</mi> <mo>\</mo> <mfenced open="{" close="}"> <mn>0</mn> </mfenced> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. This introduced a <i>q</i>-integral operator and certain subclasses of the newly introduced classes are defined by using this <i>q</i>-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>δ</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo></mrow></semantics></math></inline-formula>-neighborhood of analytic functions are introduced and the inclusion relations between the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>δ</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo></mrow></semantics></math></inline-formula>-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.https://www.mdpi.com/2073-8994/11/5/719Geometric Function Theory<i>q</i>-integral operator<i>q</i>-starlike functions of complex order<i>q</i>-convex functions of complex order(<i>δ</i>,<i>q</i>)-neighborhood |
| spellingShingle | Shahid Mahmood Nusrat Raza Eman S. A. AbuJarad Gautam Srivastava H. M. Srivastava Sarfraz Nawaz Malik Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator Symmetry Geometric Function Theory <i>q</i>-integral operator <i>q</i>-starlike functions of complex order <i>q</i>-convex functions of complex order (<i>δ</i>,<i>q</i>)-neighborhood |
| title | Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator |
| title_full | Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator |
| title_fullStr | Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator |
| title_full_unstemmed | Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator |
| title_short | Geometric Properties of Certain Classes of Analytic Functions Associated with a <i>q</i>-Integral Operator |
| title_sort | geometric properties of certain classes of analytic functions associated with a i q i integral operator |
| topic | Geometric Function Theory <i>q</i>-integral operator <i>q</i>-starlike functions of complex order <i>q</i>-convex functions of complex order (<i>δ</i>,<i>q</i>)-neighborhood |
| url | https://www.mdpi.com/2073-8994/11/5/719 |
| work_keys_str_mv | AT shahidmahmood geometricpropertiesofcertainclassesofanalyticfunctionsassociatedwithaiqiintegraloperator AT nusratraza geometricpropertiesofcertainclassesofanalyticfunctionsassociatedwithaiqiintegraloperator AT emansaabujarad geometricpropertiesofcertainclassesofanalyticfunctionsassociatedwithaiqiintegraloperator AT gautamsrivastava geometricpropertiesofcertainclassesofanalyticfunctionsassociatedwithaiqiintegraloperator AT hmsrivastava geometricpropertiesofcertainclassesofanalyticfunctionsassociatedwithaiqiintegraloperator AT sarfraznawazmalik geometricpropertiesofcertainclassesofanalyticfunctionsassociatedwithaiqiintegraloperator |