Some integral inequalities via new family of preinvex functions

Muhammad Tariq; Soubhagya Kumar Sahoo; Hijaz Ahmad; Asif Ali Shaikh; Bibhakar Kodamasingh; Dawood Khan

doi:10.53391/mmnsa.2022.010

Authors

Muhammad Tariq Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan https://orcid.org/0000-0001-8372-2532
Soubhagya Kumar Sahoo Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, Odisha, India https://orcid.org/0000-0003-4524-1951
Hijaz Ahmad Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy https://orcid.org/0000-0002-5438-5407
Asif Ali Shaikh Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan https://orcid.org/0000-0002-3084-922X
Bibhakar Kodamasingh Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, Odisha, India https://orcid.org/0000-0002-2751-7793
Dawood Khan Department of Mathematics, University of Balochistan, 87300 Pakistan https://orcid.org/0000-0002-6850-6783

DOI:

https://doi.org/10.53391/mmnsa.2022.010

Keywords:

Preinvex function, s-type preinvexity, s-type m-preinvexity, Hermite-Hadamard inequality

Abstract

The main objective of this work is to introduce and define the concept of s-type m-preinvex function and derive the new sort of Hermite-Hadamard inequality via the newly discussed idea. Furthermore, to enhance the quality of paper, we prove two new lemmas and in order to these lemmas, we attain some extensions of Hermite-Hadamard-type inequality in the manner of newly explored definition. The concepts and tools of this paper may invigorate and revitalize for additional research in this mesmerizing and absorbing field of mathematics.

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