New Parameterized Inequalities for η-Quasiconvex Functions via (p, q)-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:	Humaira Kalsoom, Miguel Vivas-Cortez, Muhammad Idrees, Praveen Agarwal
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	quantum calculus post quantum calculus parameterized (<i>p</i>, <i>q</i>)-estimates for midpoint and trapezoidal type inequalities <i>η</i>-quasiconvexity Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/84180b2a4c1846fa952bc556e690029e
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spelling	oai:doaj.org-article:84180b2a4c1846fa952bc556e690029e2021-11-25T17:30:29ZNew Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus10.3390/e231115231099-4300https://doaj.org/article/84180b2a4c1846fa952bc556e690029e2021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1523https://doaj.org/toc/1099-4300In 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.Humaira KalsoomMiguel Vivas-CortezMuhammad IdreesPraveen AgarwalMDPI AGarticlequantum calculuspost quantum calculusparameterized (<i>p</i>, <i>q</i>)-estimates for midpoint and trapezoidal type inequalities<i>η</i>-quasiconvexityScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1523, p 1523 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	quantum calculus post quantum calculus parameterized (<i>p</i>, <i>q</i>)-estimates for midpoint and trapezoidal type inequalities <i>η</i>-quasiconvexity Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	quantum calculus post quantum calculus parameterized (<i>p</i>, <i>q</i>)-estimates for midpoint and trapezoidal type inequalities <i>η</i>-quasiconvexity Science Q Astrophysics QB460-466 Physics QC1-999 Humaira Kalsoom Miguel Vivas-Cortez Muhammad Idrees Praveen Agarwal New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
description	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.
format	article
author	Humaira Kalsoom Miguel Vivas-Cortez Muhammad Idrees Praveen Agarwal
author_facet	Humaira Kalsoom Miguel Vivas-Cortez Muhammad Idrees Praveen Agarwal
author_sort	Humaira Kalsoom
title	New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
title_short	New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
title_full	New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
title_fullStr	New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
title_full_unstemmed	New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus
title_sort	new parameterized inequalities for <i>η</i>-quasiconvex functions via (<i>p</i>, <i>q</i>)-calculus
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/84180b2a4c1846fa952bc556e690029e
work_keys_str_mv	AT humairakalsoom newparameterizedinequalitiesforiēiquasiconvexfunctionsviaipiiqicalculus AT miguelvivascortez newparameterizedinequalitiesforiēiquasiconvexfunctionsviaipiiqicalculus AT muhammadidrees newparameterizedinequalitiesforiēiquasiconvexfunctionsviaipiiqicalculus AT praveenagarwal newparameterizedinequalitiesforiēiquasiconvexfunctionsviaipiiqicalculus
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New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus

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