New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
In this work, first, we consider novel parameterized identities for the left and right part of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,<...
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| Autores principales: | , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/84180b2a4c1846fa952bc556e690029e |
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| Sumario: | In this work, first, we consider novel parameterized identities for the left and right part of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-trapezoid and parameterized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-midpoint type integral inequalities via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-quasiconvex function. By changing values of parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>, some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained. |
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