New versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals

Saira Bano Akbar; Mujahid Abbas; Waqas Nazeer; Hüseyin Budak

doi:10.1186/s13661-024-01970-z

New versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals

Saira Bano Akbar
, Mujahid Abbas
, Waqas Nazeer
, Hüseyin Budak

Construction Management and Quantity Surveying

Research output: Contribution to journal › Comment/debate

Abstract

In this paper, we prove some new versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals. For this aim, we use the tangent and secant lines at the same special points. Moreover, we investigate the relations between the newly obtained results and earlier published papers. We also present some new results by special choices of ϕ and h.

Original language	English
Article number	156
Journal	Boundary Value Problems
Volume	2024
Issue number	1
DOIs	https://doi.org/10.1186/s13661-024-01970-z
Publication status	Published - Dec 2024

Keywords

(ϕ−h)-derivative
(ϕ−h)-integral
Convex function
Hermite–Hadamard Inequality

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1186/s13661-024-01970-z

Cite this

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title = "New versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals",

abstract = "In this paper, we prove some new versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals. For this aim, we use the tangent and secant lines at the same special points. Moreover, we investigate the relations between the newly obtained results and earlier published papers. We also present some new results by special choices of ϕ and h.",

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AU - Akbar, Saira Bano

AU - Abbas, Mujahid

AU - Nazeer, Waqas

AU - Budak, Hüseyin

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper, we prove some new versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals. For this aim, we use the tangent and secant lines at the same special points. Moreover, we investigate the relations between the newly obtained results and earlier published papers. We also present some new results by special choices of ϕ and h.

AB - In this paper, we prove some new versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals. For this aim, we use the tangent and secant lines at the same special points. Moreover, we investigate the relations between the newly obtained results and earlier published papers. We also present some new results by special choices of ϕ and h.

KW - (ϕ−h)-derivative

KW - (ϕ−h)-integral

KW - Convex function

KW - Hermite–Hadamard Inequality

UR - https://www.scopus.com/pages/publications/85209730432

U2 - 10.1186/s13661-024-01970-z

DO - 10.1186/s13661-024-01970-z

M3 - Comment/debate

AN - SCOPUS:85209730432

SN - 1687-2762

VL - 2024

JO - Boundary Value Problems

JF - Boundary Value Problems

IS - 1

M1 - 156

ER -

New versions of the Hermite–Hadamard inequality for (ϕ−h)-integrals

Abstract

Keywords

ASJC Scopus subject areas

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