Jensen's type inequalities for two times differentiable functions with applications

Muhammad Adil Khan; Shahid Khan; Dilda Pečarić; Josip Pečarić

Makale detayları

Jensen's type inequalities for two times differentiable functions with applications

Yazarlar:

Muhammad Adil Khan | Shahid Khan | Dilda Pečarić | Josip Pečarić

Yayıncı:

Ankara University

Ana Başlıklar:

Algebra and Number Theory

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.424-445

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357874

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 In the main body, first of all this work recommends an inequality of Jensens type involving Green functions for a class of two times differentiable functions. This result enables further to obtain some related interpolating inequalities for a function f such that fq is either concave or convex for qgeq1. Then manipulation of certain existing results in the corresponding interpolating inequalities gives bounds for the differences of the Jensen-Steffensen and Jensens inequalities. In the similar fashion, they provide some new variants for the reverse form of aforementioned inequalities. Further, the obtained results about Jensens inequality yield different novel adaptations of Hölders inequality, fresh insights into the discrepancy of the well known Hermite-Hadamard inequality, and inequalities for geometric mean, quasi-arithmetic mean, and power mean. As a resultant, this work also suggests graphical interpretation of some results to verify the authenticity and sharpness of the obtained results about Jensens inequality. Finally, this research work put forward some applications involving Zipf-Mandelbrot entropy and various types of Csiszár divergence from information theory.

 In the main body, first of all this work recommends an inequality of Jensens type involving Green functions for a class of two times differentiable functions. This result enables further to obtain some related interpolating inequalities for a function f such that fq is either concave or convex for qgeq1. Then manipulation of certain existing results in the corresponding interpolating inequalities gives bounds for the differences of the Jensen-Steffensen and Jensens inequalities. In the similar fashion, they provide some new variants for the reverse form of aforementioned inequalities. Further, the obtained results about Jensens inequality yield different novel adaptations of Hölders inequality, fresh insights into the discrepancy of the well known Hermite-Hadamard inequality, and inequalities for geometric mean, quasi-arithmetic mean, and power mean. As a resultant, this work also suggests graphical interpretation of some results to verify the authenticity and sharpness of the obtained results about Jensens inequality. Finally, this research work put forward some applications involving Zipf-Mandelbrot entropy and various types of Csiszár divergence from information theory.

 In the main body, first of all this work recommends an inequality of Jensens type involving Green functions for a class of two times differentiable functions. This result enables further to obtain some related interpolating inequalities for a function f such that fq is either concave or convex for qgeq1. Then manipulation of certain existing results in the corresponding interpolating inequalities gives bounds for the differences of the Jensen-Steffensen and Jensens inequalities. In the similar fashion, they provide some new variants for the reverse form of aforementioned inequalities. Further, the obtained results about Jensens inequality yield different novel adaptations of Hölders inequality, fresh insights into the discrepancy of the well known Hermite-Hadamard inequality, and inequalities for geometric mean, quasi-arithmetic mean, and power mean. As a resultant, this work also suggests graphical interpretation of some results to verify the authenticity and sharpness of the obtained results about Jensens inequality. Finally, this research work put forward some applications involving Zipf-Mandelbrot entropy and various types of Csiszár divergence from information theory.

 In the main body, first of all this work recommends an inequality of Jensens type involving Green functions for a class of two times differentiable functions. This result enables further to obtain some related interpolating inequalities for a function f such that fq is either concave or convex for qgeq1. Then manipulation of certain existing results in the corresponding interpolating inequalities gives bounds for the differences of the Jensen-Steffensen and Jensens inequalities. In the similar fashion, they provide some new variants for the reverse form of aforementioned inequalities. Further, the obtained results about Jensens inequality yield different novel adaptations of Hölders inequality, fresh insights into the discrepancy of the well known Hermite-Hadamard inequality, and inequalities for geometric mean, quasi-arithmetic mean, and power mean. As a resultant, this work also suggests graphical interpretation of some results to verify the authenticity and sharpness of the obtained results about Jensens inequality. Finally, this research work put forward some applications involving Zipf-Mandelbrot entropy and various types of Csiszár divergence from information theory.

Makale detayları

Jensen's type inequalities for two times differentiable functions with applications

Yazarlar:

Muhammad Adil Khan | Shahid Khan | Dilda Pečarić | Josip Pečarić

Yayıncı:

Ankara University

Ana Başlıklar:

Algebra and Number Theory

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.424-445

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357874

pISSN:

1303-5991

Jensen inequality

Green function

Jensen-Steffensen inequality

divergences

Sayı

Makale detayları

Jensen's type inequalities for two times differentiable functions with applications

Yazarlar: Muhammad Adil Khan | Shahid Khan | Dilda Pečarić | Josip Pečarić

Yayıncı: Ankara University

Ana Başlıklar: Algebra and Number Theory

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.424-445

Belge Tipi: Makale

Yayın Tarihi: 9/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001357874

pISSN: 1303-5991

Jensen inequality

Green function

Jensen-Steffensen inequality

divergences

Sayı

Yazarlar:

Muhammad Adil Khan | Shahid Khan | Dilda Pečarić | Josip Pečarić

Yayıncı:

Ankara University

Ana Başlıklar:

Algebra and Number Theory

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.424-445

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357874

pISSN:

1303-5991