Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications
In this paper, the authors investigated the concept of s,m-exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8672710 |
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| author | Artion Kashuri Sajid Iqbal Saad Ihsan Butt Jamshed Nasir Kottakkaran Sooppy Nisar Thabet Abdeljawad |
| author_facet | Artion Kashuri Sajid Iqbal Saad Ihsan Butt Jamshed Nasir Kottakkaran Sooppy Nisar Thabet Abdeljawad |
| author_sort | Artion Kashuri |
| collection | DOAJ |
| description | In this paper, the authors investigated the concept of s,m-exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and ϕ are proved. Many refinements of the (H–H) inequality via s,m-exponential-type convex are obtained. Finally, several new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences. |
| format | Article |
| id | doaj-art-a109be22e2d44d51b98800e0f392c1ea |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a109be22e2d44d51b98800e0f392c1ea2025-02-03T05:52:30ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/86727108672710Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their ApplicationsArtion Kashuri0Sajid Iqbal1Saad Ihsan Butt2Jamshed Nasir3Kottakkaran Sooppy Nisar4Thabet Abdeljawad5Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, AlbaniaDepartment of Mathematics, Riphah International University, Faisalabad Campus, Satyana Road, Faisalabad, PakistanComsats University Islamabad, Lahore Campus, Lahore, PakistanVirtual University of Pakistan, Lahore Campus, Lahore, PakistanDepartment of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh 12345, Saudi ArabiaIn this paper, the authors investigated the concept of s,m-exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and ϕ are proved. Many refinements of the (H–H) inequality via s,m-exponential-type convex are obtained. Finally, several new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences.http://dx.doi.org/10.1155/2020/8672710 |
| spellingShingle | Artion Kashuri Sajid Iqbal Saad Ihsan Butt Jamshed Nasir Kottakkaran Sooppy Nisar Thabet Abdeljawad Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications Journal of Mathematics |
| title | Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications |
| title_full | Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications |
| title_fullStr | Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications |
| title_full_unstemmed | Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications |
| title_short | Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications |
| title_sort | trapezium type inequalities for k fractional integral via new exponential type convexity and their applications |
| url | http://dx.doi.org/10.1155/2020/8672710 |
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