Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator
Using the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-Sălăgean operator, we introduce a new...
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2025-05-01
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| author | Ekram E. Ali Rabha M. El-Ashwah Teodor Bulboacă Abeer M. Albalahi |
| author_facet | Ekram E. Ali Rabha M. El-Ashwah Teodor Bulboacă Abeer M. Albalahi |
| author_sort | Ekram E. Ali |
| collection | DOAJ |
| description | Using the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-Sălăgean operator, we introduce a new class of meromorphic functions in a punctured unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="script">U</mi><mo>∗</mo></msup></semantics></math></inline-formula> and investigate a majorization problem associated with this class. The principal tool employed in this analysis is the recently established <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-Schwarz–Pick lemma. We investigate a majorization problem for meromorphic functions when the functions of the right hand side of the majorization belongs to this class. The main tool for this investigation is the generalization of Nehari’s lemma for the Jackson’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-difference operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>∂</mo><mi mathvariant="fraktur">q</mi></msub></semantics></math></inline-formula> given recently by Adegani et al. |
| format | Article |
| id | doaj-art-8f35ede34d194d34b15691b739ccf032 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-8f35ede34d194d34b15691b739ccf0322025-08-20T03:14:36ZengMDPI AGMathematics2227-73902025-05-011310161210.3390/math13101612Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean OperatorEkram E. Ali0Rabha M. El-Ashwah1Teodor Bulboacă2Abeer M. Albalahi3Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, EgyptResearch Center of Applied Analysis, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaDepartment of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi ArabiaUsing the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-Sălăgean operator, we introduce a new class of meromorphic functions in a punctured unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="script">U</mi><mo>∗</mo></msup></semantics></math></inline-formula> and investigate a majorization problem associated with this class. The principal tool employed in this analysis is the recently established <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-Schwarz–Pick lemma. We investigate a majorization problem for meromorphic functions when the functions of the right hand side of the majorization belongs to this class. The main tool for this investigation is the generalization of Nehari’s lemma for the Jackson’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-difference operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>∂</mo><mi mathvariant="fraktur">q</mi></msub></semantics></math></inline-formula> given recently by Adegani et al.https://www.mdpi.com/2227-7390/13/10/1612meromorphic functionsubordinationconvolutionmajorization problemJackson’s <named-content content-type="inline"><inline-formula> <mml:math id="mm451"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-difference operatorgeneralized <named-content content-type="inline"><inline-formula> <mml:math id="mm561"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-Sălăgean operator |
| spellingShingle | Ekram E. Ali Rabha M. El-Ashwah Teodor Bulboacă Abeer M. Albalahi Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator Mathematics meromorphic function subordination convolution majorization problem Jackson’s <named-content content-type="inline"><inline-formula> <mml:math id="mm451"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-difference operator generalized <named-content content-type="inline"><inline-formula> <mml:math id="mm561"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-Sălăgean operator |
| title | Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator |
| title_full | Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator |
| title_fullStr | Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator |
| title_full_unstemmed | Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator |
| title_short | Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mi mathvariant="fraktur">q</mi></mstyle></semantics></math></inline-formula>-Sălăgean Operator |
| title_sort | majorization problems for subclasses of meromorphic functions defined by the generalized inline formula math display inline semantics mstyle mathvariant bold mi mathvariant fraktur q mi mstyle semantics math inline formula salagean operator |
| topic | meromorphic function subordination convolution majorization problem Jackson’s <named-content content-type="inline"><inline-formula> <mml:math id="mm451"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-difference operator generalized <named-content content-type="inline"><inline-formula> <mml:math id="mm561"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-Sălăgean operator |
| url | https://www.mdpi.com/2227-7390/13/10/1612 |
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