The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function

Gültekin Tınaztepe; Sinem Sezer Evcan; Zeynep Eken; Sevda Sezer

Article Details

The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function

Authors:

Gültekin Tınaztepe | Sinem Sezer Evcan | Zeynep Eken | Sevda Sezer

Publisher:

Hacettepe University

Main Topics:

Applied Mathematics (Other)

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.404-413

Document Type:

Article

Publication Date:

4/2025

Document Language:

English

Document ID (Org No.):

2001346362

pISSN:

2651-477X

Keywords:

Abstract:

 By means of an integral identity, several Hermite-Hadamard type inequalities are presented in this study for a function whose derivatives absolute value is the log-p-convex function. With the use of these findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error function, the exponential integral, the hyperbolic sine and cosine functions. Additionally, a relationship between beta function, the hyperbolic sine and cosine functions is stated. Through the obtained results, a bound for numerical integration of such type functions is provided.

 By means of an integral identity, several Hermite-Hadamard type inequalities are presented in this study for a function whose derivatives absolute value is the log-p-convex function. With the use of these findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error function, the exponential integral, the hyperbolic sine and cosine functions. Additionally, a relationship between beta function, the hyperbolic sine and cosine functions is stated. Through the obtained results, a bound for numerical integration of such type functions is provided.

 By means of an integral identity, several Hermite-Hadamard type inequalities are presented in this study for a function whose derivatives absolute value is the log-p-convex function. With the use of these findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error function, the exponential integral, the hyperbolic sine and cosine functions. Additionally, a relationship between beta function, the hyperbolic sine and cosine functions is stated. Through the obtained results, a bound for numerical integration of such type functions is provided.

 By means of an integral identity, several Hermite-Hadamard type inequalities are presented in this study for a function whose derivatives absolute value is the log-p-convex function. With the use of these findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error function, the exponential integral, the hyperbolic sine and cosine functions. Additionally, a relationship between beta function, the hyperbolic sine and cosine functions is stated. Through the obtained results, a bound for numerical integration of such type functions is provided.

Article Details

The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function

Authors:

Gültekin Tınaztepe | Sinem Sezer Evcan | Zeynep Eken | Sevda Sezer

Publisher:

Hacettepe University

Main Topics:

Applied Mathematics (Other)

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.404-413

Document Type:

Article

Publication Date:

4/2025

Document Language:

English

Document ID (Org No.):

2001346362

pISSN:

2651-477X

p-convex set

log p-convex function

p-convex function

Hermite-Hadamard inequality

Issues

Article Details

The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function

Authors: Gültekin Tınaztepe | Sinem Sezer Evcan | Zeynep Eken | Sevda Sezer

Publisher: Hacettepe University

Main Topics: Applied Mathematics (Other)

Journal: Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.404-413

Document Type: Article

Publication Date: 4/2025

Document Language: English

Document ID (Org No.): 2001346362

pISSN: 2651-477X

p-convex set

log p-convex function

p-convex function

Hermite-Hadamard inequality

Issues

Authors:

Gültekin Tınaztepe | Sinem Sezer Evcan | Zeynep Eken | Sevda Sezer

Publisher:

Hacettepe University

Main Topics:

Applied Mathematics (Other)

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.404-413

Document Type:

Article

Publication Date:

4/2025

Document Language:

English

Document ID (Org No.):

2001346362

pISSN:

2651-477X