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

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

Makale detayları

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

Yazarlar:

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

Yayıncı:

Hacettepe University

Ana Başlıklar:

Applied Mathematics (Other)

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346362

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 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.

Makale detayları

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

Yazarlar:

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

Yayıncı:

Hacettepe University

Ana Başlıklar:

Applied Mathematics (Other)

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346362

pISSN:

2651-477X

p-convex set

log p-convex function

p-convex function

Hermite-Hadamard inequality

Sayı

Makale detayları

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

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

Yayıncı: Hacettepe University

Ana Başlıklar: Applied Mathematics (Other)

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

Belge Tipi: Makale

Yayın Tarihi: 4/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001346362

pISSN: 2651-477X

p-convex set

log p-convex function

p-convex function

Hermite-Hadamard inequality

Sayı

Yazarlar:

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

Yayıncı:

Hacettepe University

Ana Başlıklar:

Applied Mathematics (Other)

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346362

pISSN:

2651-477X