New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications
Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski typ...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/8/1429 |
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| author | Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Jamshed Nasir Hassen Aydi Aiman Mukheimer |
| author_facet | Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Jamshed Nasir Hassen Aydi Aiman Mukheimer |
| author_sort | Soubhagya Kumar Sahoo |
| collection | DOAJ |
| description | Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, <i>n</i>–polynomial exponentially <i>s</i>–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature. |
| first_indexed | 2024-03-10T08:20:10Z |
| format | Article |
| id | doaj.art-18281e2b41774375ba0cb63ab6a5aa60 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:20:10Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-18281e2b41774375ba0cb63ab6a5aa602023-11-22T10:01:21ZengMDPI AGSymmetry2073-89942021-08-01138142910.3390/sym13081429New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and ApplicationsSoubhagya Kumar Sahoo0Muhammad Tariq1Hijaz Ahmad2Jamshed Nasir3Hassen Aydi4Aiman Mukheimer5Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, PakistanSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Roma, ItalyDepartment of Mathematics & Statistics, Virtual University of Pakistan, Lahore Campus 54000, PakistanInstitut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, Hammam Sousse 4000, TunisiaDepartment of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi ArabiaRecently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, <i>n</i>–polynomial exponentially <i>s</i>–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.https://www.mdpi.com/2073-8994/13/8/1429Ostrowski inequalityHölder’s inequalitypower mean integral inequalityn-polynomial exponentially s-convex function |
| spellingShingle | Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Jamshed Nasir Hassen Aydi Aiman Mukheimer New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications Symmetry Ostrowski inequality Hölder’s inequality power mean integral inequality n-polynomial exponentially s-convex function |
| title | New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications |
| title_full | New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications |
| title_fullStr | New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications |
| title_full_unstemmed | New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications |
| title_short | New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications |
| title_sort | new ostrowski type fractional integral inequalities via generalized exponential type convex functions and applications |
| topic | Ostrowski inequality Hölder’s inequality power mean integral inequality n-polynomial exponentially s-convex function |
| url | https://www.mdpi.com/2073-8994/13/8/1429 |
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