A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions
Volume 26, Issue 4, pp 330--348
http://dx.doi.org/10.22436/jmcs.026.04.02
Publication Date: December 08, 2021
Submission Date: September 03, 2021
Revision Date: September 23, 2021
Accteptance Date: November 23, 2021
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Authors
M. Tariq
- Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan.
H. Ahmad
- Department of Computer Engineering, Biruni University, Istanbul 34025, Turkey.
- Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 , Roma, Italy.
S. K. Sahoo
- Department of Mathematics, Institute of Technical Education and Research, Siksha `O' Anusandhan University, Bhubaneswar 751030, India.
L. Sh. Aljoufi
- Deanship of Common First Year, Jouf University, P.O.Box 2014 Sakaka, Saudi Arabia.
- Basic Sciences Research Unit, Jouf University, P.O.Box 2014 Sakaka, Saudi Arabia.
S. K. Awan
- Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan.
Abstract
The main objective of this article is to employ the concept of preinvexity to establish some new inequalities. In addition, we discuss some algebraic properties and examples of the generalized preinvex function. With the help of this new relation, we present new version of Hermite-Hadamard inequality and its some of its refinements using fundamental inequalities like Hölder, power-mean, Hölder-Iscan, and improved power-mean inequality. These results are speculations of various recently known outcomes. The immeasurable concepts and tools of this paper may invigorate and revitalize for additional research in this mesmerizing and absorbing field.
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ISRP Style
M. Tariq, H. Ahmad, S. K. Sahoo, L. Sh. Aljoufi, S. K. Awan, A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions, Journal of Mathematics and Computer Science, 26 (2022), no. 4, 330--348
AMA Style
Tariq M., Ahmad H., Sahoo S. K., Aljoufi L. Sh., Awan S. K., A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions. J Math Comput SCI-JM. (2022); 26(4):330--348
Chicago/Turabian Style
Tariq, M., Ahmad, H., Sahoo, S. K., Aljoufi, L. Sh., Awan, S. K.. "A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions." Journal of Mathematics and Computer Science, 26, no. 4 (2022): 330--348
Keywords
- \(s\)-type convex function
- preinvex function
- \(m\)-preinvex function
- Hölder's inequality
- Hölder-Iscan integral inequality
- power mean inequality
- improved power-mean integral inequality
MSC
- 26A51
- 26A33
- 26D07
- 26D10
- 26D15
References
-
[1]
H. Ahmad, M. Tariq, S. K. Sahoo, J. Baili, C. Cesarano, New estimations of Hermite--Hadamard type integral inequalities for special functions, Fractal Fract., 5 (2021), 26 pages
-
[2]
T. Antczak, Mean value in invexity analysis, Nonlinear Anal., 60 (2005), 1473--1484
-
[3]
M. U. Awan, S. Talib, M. A. Noor, Y.-M. Chu, K. I. Noor, Some trapezium--like inequalities involving functions having strongly $n$--polynomial preinvexity property of higher order, J. Funct. Spaces, 2020 (2020), 9 pages
-
[4]
G. Barani, Ghazanfari, S. S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl., 2012 (2012), 9 pages
-
[5]
S. I. Butt, A. Kashuri, M. Tariq, J. Nasir, A. Aslam, W. Geo, Hermite-Hadamard-type inequalities via $n$-polynomial exponential-type convexity and their applications, Adv. Difference Equ., 2020 (2020), 25 pages
-
[6]
S. I. Butt, A. Kashuri, M. Tariq, J. Nasir, A. Aslam, W. Geo, $n$--polynomial exponential--type $p$--convex function with some related inequalities and their application, Heliyon, 6 (2020), 9 pages
-
[7]
S. I. Butt, M. Nadeem, S. Qaisar, A. O. Akdemir, T. Abdeljawad, Hermite--Jensen--Mercer type inequalities for conformable integrals and related results, Adv. Difference Equ., 2020 (2020), 24 pages
-
[8]
S. I. Butt, M. Tariq, A. Aslam, H. Ahmad, T. A. Nofel, Hermite-Hadamard type inequalities via generalized harmonic exponential convexity and applications, J. Funct. Spaces, 2021 (2021), 12 pages
-
[9]
Y. P. Deng, H. Kalsoom, S. H. Wu, Some new Quantum Hermite–Hadamard-type estimates within a class of generalized $(s,m)$--preinvex functions, Symmetry, 11 (2019), 15 pages
-
[10]
T.-S. Du, J.-G. Liao, Y.-J. Li, Properties and integral inequalities of Hadamard--Simpson type for the generalized $(s,m)$--preinvex functions, J. Nonlinear Sci. Appl., 9 (2016), 3112--3126
-
[11]
J. Hadamard, Etude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171--215
-
[12]
M. A. Khan, Y. M. Chu, T. U. Khan, J. Khan, Some new inequalities of Hermite-Hadamard type for $s$-convex functions with applications, Open Math., 15 (2017), 1414--1430
-
[13]
S. Kumari, M. Kumari, R. Chugh, Generation of new fractals via SP orbit with $s$--convexity, Int. J. Eng. Technol., 9 (2017), 2491--2504
-
[14]
Y. C. Kwun, A. A. Shahid, W. Nazeer, M. Abbas, S. M. Kang, Fractal generation via CR iteration scheme with $s$--convexity, IEEE Access, 7 (2019), 69986--69997
-
[15]
M. A. Latif, M. Shoaib, Hermite-Hadamard type integral inequalities for differentiable $m$-preinvex and $(\alpha,m)$-preinvex functions, J. Egyptian Math. Soc., 23 (2015), 236--241
-
[16]
S. Mititelu, Invex sets, Stud. Cerc. Mat., 46 (1994), 529--532
-
[17]
S. R. Mohan, S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901--908
-
[18]
C. P. Niculescu, L.-E. Persson, Convex functions and their applications, Springer-Verlag, New York (2006)
-
[19]
M. A. Noor, On Hadamard integral inequalities invoving two log-preinvex functions, J. Inequal. Pure. Appl. Math., 8 (2007), 14 pages
-
[20]
M. A. Noor, Hadamard integral inequalities for product of two preinvex function, Nonlinear Anal. Forum, 14 (2009), 167--173
-
[21]
M. A. Noor, K. I. Noor, M. U. Awan, J. Y. Li, On Hermite-Hadamard inequalities for $h$-preinvex functions, Filomat, 28 (2014), 1463--1474
-
[22]
S. Özcan, İ. İşcan, Some new Hermite-Hadamard type integral inequalities for the $s$--convex functions and theirs applications, J. Inequal. Appl., 201 (2019), 1--14
-
[23]
S. Rashid, İ. İşcan, D. Baleanu, Y.-M. Chu, Generation of new fractional inequalities via $n$--polynomials $s$--type convexity with applications, Adv. Difference Equ., 2020 (2020), 20 pages
-
[24]
S. K. Sahoo, H. Ahmad, M. Tariq, B. Kodamasingh, H. Aydi, M. De la Sen, Hermite--Hadamard type inequalities involving k-fractional operator for $(\bar{h},m)$-convex Functions, Symmetry, 13 (2021), 16 pages
-
[25]
S. K. Sahoo, M. Tariq, H. Ahmad, J. Nasir, H. Aydi, A. Mukheimer, New Ostrowski-type fractional integral inequalities via generalized exponential-type convex functions and applications, Symmetry, 13 (2021), 18 pages
-
[26]
H. J. Skala, On the characterization of certain similarly ordered super-additive functionals, Proc. Amer. Math. Soc., 126 (1998), 1349--1353
-
[27]
G. H. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim (Cluj-Napoca, Romania), 1985 (1985), 329--338
-
[28]
T. Toplu, M. Kadakal, İ. İşcan, On $n$--polynomial convexity and some related inequalities, AIMS Math., 5 (2020), 1304--1318
-
[29]
T. Weir, B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl., 136 (1988), 29--38
-
[30]
B.-Y. Xi, F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl., 2012 (2012), 14 pages