New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators
As the most important inequality, the Hermite–Hadamard–Mercer inequality has attracted the interest of numerous additional mathematicians. Numerous findings on this inequality have been developed in recent years. So, in this paper, we demonstrate novel Hermite–Hadamard–Mercer inequalities using Rain...
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2025-05-01
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| author | Çetin Yildiz Tevfik İşleyen Luminiţa-Ioana Cotîrlă |
| author_facet | Çetin Yildiz Tevfik İşleyen Luminiţa-Ioana Cotîrlă |
| author_sort | Çetin Yildiz |
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| description | As the most important inequality, the Hermite–Hadamard–Mercer inequality has attracted the interest of numerous additional mathematicians. Numerous findings on this inequality have been developed in recent years. So, in this paper, we demonstrate novel Hermite–Hadamard–Mercer inequalities using Raina fractional operators and the majorization concept. Furthermore, additional identities are discovered, and two new lemmas of this type are proved. A summary of several known results is also provided, along with a thorough derivation of some exceptional cases. We also note that some of the outcomes in this study are more acceptable than others under certain exceptional instances, such as setting <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mi>α</mi></mrow></semantics></math></inline-formula>. Lastly, the method described in this publication is thought to stimulate further research in this area. |
| format | Article |
| id | doaj-art-5bdcfcd51ad04096ba74718150fd59bc |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
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| series | Fractal and Fractional |
| spelling | doaj-art-5bdcfcd51ad04096ba74718150fd59bc2025-08-20T02:21:09ZengMDPI AGFractal and Fractional2504-31102025-05-019634310.3390/fractalfract9060343New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional OperatorsÇetin Yildiz0Tevfik İşleyen1Luminiţa-Ioana Cotîrlă2Department of Mathematics, K.K. Education Faculty, Atatürk University, 25240 Erzurum, TurkeyDepartment of Mathematics, K.K. Education Faculty, Atatürk University, 25240 Erzurum, TurkeyDepartment of Mathematics, Technical University of Cluj-Napoca, 400020 Cluj-Napoca, RomaniaAs the most important inequality, the Hermite–Hadamard–Mercer inequality has attracted the interest of numerous additional mathematicians. Numerous findings on this inequality have been developed in recent years. So, in this paper, we demonstrate novel Hermite–Hadamard–Mercer inequalities using Raina fractional operators and the majorization concept. Furthermore, additional identities are discovered, and two new lemmas of this type are proved. A summary of several known results is also provided, along with a thorough derivation of some exceptional cases. We also note that some of the outcomes in this study are more acceptable than others under certain exceptional instances, such as setting <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mi>α</mi></mrow></semantics></math></inline-formula>. Lastly, the method described in this publication is thought to stimulate further research in this area.https://www.mdpi.com/2504-3110/9/6/343Hermite–Hadamard inequalityJensen–Mercer inequalitymajorizationRaina fractional operator |
| spellingShingle | Çetin Yildiz Tevfik İşleyen Luminiţa-Ioana Cotîrlă New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators Fractal and Fractional Hermite–Hadamard inequality Jensen–Mercer inequality majorization Raina fractional operator |
| title | New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators |
| title_full | New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators |
| title_fullStr | New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators |
| title_full_unstemmed | New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators |
| title_short | New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators |
| title_sort | new results on majorized discrete jensen mercer inequality for raina fractional operators |
| topic | Hermite–Hadamard inequality Jensen–Mercer inequality majorization Raina fractional operator |
| url | https://www.mdpi.com/2504-3110/9/6/343 |
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