New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems

In the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as the ψ-s-convex and ψ-quasi-convex functions. As a result, some refinements of the Hermite–Hadamard (ℋℋ{\mathcal{ {\mathcal H} {\mathcal H} }})-type inequalities regarding ou...

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Autores principales:	Rashid Saima, Parveen Saima, Ahmad Hijaz, Chu Yu-Ming
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	quantum estimates hermite–hadamard inequalities convex functions generalized ψ-convex functions raina function Physics QC1-999
Acceso en línea:	https://doaj.org/article/7eb4745d7ad946ff9e6541b6f8cb8921
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id	oai:doaj.org-article:7eb4745d7ad946ff9e6541b6f8cb8921
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spelling	oai:doaj.org-article:7eb4745d7ad946ff9e6541b6f8cb89212021-12-05T14:11:01ZNew quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems2391-547110.1515/phys-2021-0001https://doaj.org/article/7eb4745d7ad946ff9e6541b6f8cb89212021-02-01T00:00:00Zhttps://doi.org/10.1515/phys-2021-0001https://doaj.org/toc/2391-5471In the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as the ψ-s-convex and ψ-quasi-convex functions. As a result, some refinements of the Hermite–Hadamard (ℋℋ{\mathcal{ {\mathcal H} {\mathcal H} }})-type inequalities regarding our proposed technique are derived via generalized ψ-quasi-convex and generalized ψ-s-convex functions. Considering an identity, several new inequalities connected to the ℋℋ{\mathcal{ {\mathcal H} {\mathcal H} }} type for twice differentiable functions for the aforesaid classes are derived. The consequences elaborated here, being very broad, are figured out to be dedicated to recapturing some known results. Appropriate links of the numerous outcomes apprehended here with those connecting comparatively with classical quasi-convex functions are also specified. Finally, the proposed study also allows the description of a process analogous to the initial and final condition description used by quantum mechanics and special relativity theory.Rashid SaimaParveen SaimaAhmad HijazChu Yu-MingDe Gruyterarticlequantum estimateshermite–hadamard inequalitiesconvex functionsgeneralized ψ-convex functionsraina functionPhysicsQC1-999ENOpen Physics, Vol 19, Iss 1, Pp 35-50 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	quantum estimates hermite–hadamard inequalities convex functions generalized ψ-convex functions raina function Physics QC1-999
spellingShingle	quantum estimates hermite–hadamard inequalities convex functions generalized ψ-convex functions raina function Physics QC1-999 Rashid Saima Parveen Saima Ahmad Hijaz Chu Yu-Ming New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
description	In the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as the ψ-s-convex and ψ-quasi-convex functions. As a result, some refinements of the Hermite–Hadamard (ℋℋ{\mathcal{ {\mathcal H} {\mathcal H} }})-type inequalities regarding our proposed technique are derived via generalized ψ-quasi-convex and generalized ψ-s-convex functions. Considering an identity, several new inequalities connected to the ℋℋ{\mathcal{ {\mathcal H} {\mathcal H} }} type for twice differentiable functions for the aforesaid classes are derived. The consequences elaborated here, being very broad, are figured out to be dedicated to recapturing some known results. Appropriate links of the numerous outcomes apprehended here with those connecting comparatively with classical quasi-convex functions are also specified. Finally, the proposed study also allows the description of a process analogous to the initial and final condition description used by quantum mechanics and special relativity theory.
format	article
author	Rashid Saima Parveen Saima Ahmad Hijaz Chu Yu-Ming
author_facet	Rashid Saima Parveen Saima Ahmad Hijaz Chu Yu-Ming
author_sort	Rashid Saima
title	New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
title_short	New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
title_full	New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
title_fullStr	New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
title_full_unstemmed	New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
title_sort	new quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/7eb4745d7ad946ff9e6541b6f8cb8921
work_keys_str_mv	AT rashidsaima newquantumintegralinequalitiesforsomenewclassesofgeneralizedpsconvexfunctionsandtheirscopeinphysicalsystems AT parveensaima newquantumintegralinequalitiesforsomenewclassesofgeneralizedpsconvexfunctionsandtheirscopeinphysicalsystems AT ahmadhijaz newquantumintegralinequalitiesforsomenewclassesofgeneralizedpsconvexfunctionsandtheirscopeinphysicalsystems AT chuyuming newquantumintegralinequalitiesforsomenewclassesofgeneralizedpsconvexfunctionsandtheirscopeinphysicalsystems
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New quantum integral inequalities for some new classes of generalized ψ-convex functions and their scope in physical systems

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