Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions
In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close="...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/1/16 |
| _version_ | 1797446185428975616 |
|---|---|
| author | Sikander Mehmood Hari Mohan Srivastava Pshtiwan Othman Mohammed Eman Al-Sarairah Fiza Zafar Kamsing Nonlaopon |
| author_facet | Sikander Mehmood Hari Mohan Srivastava Pshtiwan Othman Mohammed Eman Al-Sarairah Fiza Zafar Kamsing Nonlaopon |
| author_sort | Sikander Mehmood |
| collection | DOAJ |
| description | In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msub><mi>ω</mi><mn>1</mn></msub><mo>,</mo><msub><mi>ω</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula>-preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msub><mi>ω</mi><mn>1</mn></msub><mo>,</mo><msub><mi>ω</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula>-preinvex functions of the positive self-adjoint operator in the complex Hilbert spaces. We give the special cases to our results; thus, the established results are generalizations of earlier work. In the last section, we give applications for synchronous (asynchronous) functions. |
| first_indexed | 2024-03-09T13:37:43Z |
| format | Article |
| id | doaj.art-fde5343aef844cedaaf23c4a97888aa7 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:37:43Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-fde5343aef844cedaaf23c4a97888aa72023-11-30T21:11:08ZengMDPI AGAxioms2075-16802022-12-011211610.3390/axioms12010016Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex FunctionsSikander Mehmood0Hari Mohan Srivastava1Pshtiwan Othman Mohammed2Eman Al-Sarairah3Fiza Zafar4Kamsing Nonlaopon5Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, IraqDepartment of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab EmiratesCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandIn this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msub><mi>ω</mi><mn>1</mn></msub><mo>,</mo><msub><mi>ω</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula>-preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msub><mi>ω</mi><mn>1</mn></msub><mo>,</mo><msub><mi>ω</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula>-preinvex functions of the positive self-adjoint operator in the complex Hilbert spaces. We give the special cases to our results; thus, the established results are generalizations of earlier work. In the last section, we give applications for synchronous (asynchronous) functions.https://www.mdpi.com/2075-1680/12/1/16Hermite–Hadamard inequalitiesHermite–Hadamard–Fejér inequalities<i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-preinvexityself-adjoint operatorspositive operatorsfunctions of self-adjoint operators |
| spellingShingle | Sikander Mehmood Hari Mohan Srivastava Pshtiwan Othman Mohammed Eman Al-Sarairah Fiza Zafar Kamsing Nonlaopon Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions Axioms Hermite–Hadamard inequalities Hermite–Hadamard–Fejér inequalities <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-preinvexity self-adjoint operators positive operators functions of self-adjoint operators |
| title | Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions |
| title_full | Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions |
| title_fullStr | Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions |
| title_full_unstemmed | Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions |
| title_short | Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-Preinvex Functions |
| title_sort | fejer type midpoint and trapezoidal inequalities for the operator i ω i sub 1 sub i ω i sub 2 sub preinvex functions |
| topic | Hermite–Hadamard inequalities Hermite–Hadamard–Fejér inequalities <i>ω</i><sub>1</sub>,<i>ω</i><sub>2</sub>-preinvexity self-adjoint operators positive operators functions of self-adjoint operators |
| url | https://www.mdpi.com/2075-1680/12/1/16 |
| work_keys_str_mv | AT sikandermehmood fejertypemidpointandtrapezoidalinequalitiesfortheoperatoriōisub1subiōisub2subpreinvexfunctions AT harimohansrivastava fejertypemidpointandtrapezoidalinequalitiesfortheoperatoriōisub1subiōisub2subpreinvexfunctions AT pshtiwanothmanmohammed fejertypemidpointandtrapezoidalinequalitiesfortheoperatoriōisub1subiōisub2subpreinvexfunctions AT emanalsarairah fejertypemidpointandtrapezoidalinequalitiesfortheoperatoriōisub1subiōisub2subpreinvexfunctions AT fizazafar fejertypemidpointandtrapezoidalinequalitiesfortheoperatoriōisub1subiōisub2subpreinvexfunctions AT kamsingnonlaopon fejertypemidpointandtrapezoidalinequalitiesfortheoperatoriōisub1subiōisub2subpreinvexfunctions |