Some Ostrowski type inequalities via $ n $-polynomial exponentially $ s $-convex functions and their applications

Muhammad Tariq; Soubhagya Kumar Sahoo; Jamshed Nasir; Hassen Aydi; Habes Alsamir; Muhammad Tariq; Soubhagya Kumar Sahoo; Jamshed Nasir; Hassen Aydi; Habes Alsamir

doi:10.3934/math.2021768

AIMS Mathematics

2021, Volume 6, Issue 12: 13272-13290. doi: 10.3934/math.2021768

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Research article

Some Ostrowski type inequalities via $ n $-polynomial exponentially $ s $-convex functions and their applications

1.
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
2.
Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, Odisha, India
3.
Virtual University Islamabad, Lahore Campus, Pakistan
4.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
6.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
7.
College of Business Administration-Finance Department, Dar Al Uloom University, Saudi Arabia

Received: 13 June 2021 Accepted: 09 September 2021 Published: 16 September 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

This paper deals with introducing and investigating a new convex mapping namely, $ n $-polynomial exponentially $ s $-convex. Here, we present some algebraic properties and some logical examples to validate the theory of newly introduced convexity. Some novel adaptations of the well-known Hermite-Hadamard and Ostrowski type inequalities for this convex function have been established. Additionally, some special cases of the newly established results are derived as well. Finally, as applications some new limits for special means of positive real numbers are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.
- Ostrowski inequality,
- Hölder's inequality,
- power-mean integral inequality,
- $ n $-polynomial exponentially $ s $-convex function
Citation: Muhammad Tariq, Soubhagya Kumar Sahoo, Jamshed Nasir, Hassen Aydi, Habes Alsamir. Some Ostrowski type inequalities via $ n $-polynomial exponentially $ s $-convex functions and their applications[J]. AIMS Mathematics, 2021, 6(12): 13272-13290. doi: 10.3934/math.2021768

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Abstract

This paper deals with introducing and investigating a new convex mapping namely, $ n $-polynomial exponentially $ s $-convex. Here, we present some algebraic properties and some logical examples to validate the theory of newly introduced convexity. Some novel adaptations of the well-known Hermite-Hadamard and Ostrowski type inequalities for this convex function have been established. Additionally, some special cases of the newly established results are derived as well. Finally, as applications some new limits for special means of positive real numbers are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.

References

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