Relative strongly harmonic convex functions and their characterizations
-
2060
Downloads
-
4061
Views
Authors
Bandar Bin-Mohsin
- Department of Mathematics, King Saud University, Riyadh, Saudi Arabia.
Muhammad Aslam Noor
- Department of Mathematics, King Saud University, Riyadh, Saudi Arabia.
- Department of Mathematics, COMSATS Institute of Information Technology, Park Road,, Islamabad, Pakistan.
Khalida Inayat Noor
- Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.
Sabah Iftikhar
- Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.
Abstract
In this paper, we introduce a new class of harmonic convex functions
with respect to an arbitrary non-negative function, which is called
the strongly general harmonic convex function. We discuss some
characterizations of strongly general harmonic convex functions.
Relationship with other classes of convex functions are also
discussed. Some special cases are discussed as applications of the
main results. The ideas and techniques of this paper may be starting
point for further research.
Share and Cite
ISRP Style
Bandar Bin-Mohsin, Muhammad Aslam Noor, Khalida Inayat Noor, Sabah Iftikhar, Relative strongly harmonic convex functions and their characterizations, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 9, 1070--1076
AMA Style
Bin-Mohsin Bandar, Aslam Noor Muhammad, Noor Khalida Inayat, Iftikhar Sabah, Relative strongly harmonic convex functions and their characterizations. J. Nonlinear Sci. Appl. (2018); 11(9):1070--1076
Chicago/Turabian Style
Bin-Mohsin, Bandar, Aslam Noor, Muhammad, Noor, Khalida Inayat, Iftikhar, Sabah. "Relative strongly harmonic convex functions and their characterizations." Journal of Nonlinear Sciences and Applications, 11, no. 9 (2018): 1070--1076
Keywords
- Harmonic convex function
- strongly harmonic convex function
- strongly general convex functions
MSC
References
-
[1]
M. Adamek, On a problem connected with strongly convex functions, Math. Inequ. Appl., 19 (2016), 1287–1293.
-
[2]
G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl., 335 (2007), 1294–1308.
-
[3]
H. Angulo, J. Gimenez, A. M. Moros, K. Nikodem, On strongly h-convex functions, Ann. Funct. Anal., 2 (2011), 85–91.
-
[4]
A. Azcar, J. Gimnez, K. Nikodem, J. L. Snchez, On strongly midconvex functions, Opuscula Math., 31 (2011), 15–26.
-
[5]
A. Azócar, K. Nikodem, G. Roa, Fejer type inequalities for strongly convex functions, Annal. Math. Siles., 26 (2012), 43–54.
-
[6]
G. Cristescu, L. Lupsa, Non-connected Convexities and Applications, Kluwer Academic Publisher, Dordrechet (2002)
-
[7]
R. Gen, K. Nikodem, Strongly convex functions of higher order, Nonlinear Anal., 74 (2011), 661–665.
-
[8]
J. Hadamard, Etude sur les proprietes des fonctions entieres e.t en particulier dune fonction consideree par Riemann, J. Math. Pure Appl., 58 (1893), 171–215.
-
[9]
C. Hermite, Sur deux limites d’une intégrale définie, Mathesis, (1883)
-
[10]
I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacett, J. Math. Stats., 43 (2014), 935– 942.
-
[11]
M. V. Jovanovic, A note on strongly convex and strongly quasiconvex functions, Math. Notes, 60 (1996), 778–779.
-
[12]
T. Lara, N. Merentes, K. Nikodem, Strong h-convexity and separation theorems, Int. J. Anal., 2016 (2016), 5 pages.
-
[13]
N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math., 80 (2010), 193–199.
-
[14]
K. Nikodem, Strongly convex functions and related classes of functions, Handbook of functional equations, 2014 (2014), 365–405.
-
[15]
K. Nikodem, Z. Pales, Characterizations of inner product spaces by strongly convex functions, Banach J. Math. Anal., 5 (2011), 83–87.
-
[16]
M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217–229.
-
[17]
M. A. Noor, Some development in general variational inequalities, Appl. Math. Comput., 152 (2004), 199–277.
-
[18]
M. A. Noor, G. Cristescu, M. U. Awan, Bounds having Riemann type quantum integrals via strongly convex functions, Studia Sci. Math. Hungar., 54 (2017), 221–240.
-
[19]
M. A. Noor, K. I. Noor, Harmonic variational inequalities, Appl. Math. Inf. Sci., 10 (2016), 1811–1814.
-
[20]
M. A. Noor, K. I. Noor, Some Implicit Methods for Solving Harmonic Variational Inequalities, Inter. J. Anal. Appl., 12 (2016), 10–14.
-
[21]
M. A. Noor, K. I. Noor, S. Iftikhar, Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Inequal. Spec. Funct., 7 (2016), 99–113.
-
[22]
M. A. Noor, K. I. Noor, S. Iftikhar, Inequalities via strongly p-harmonic log-convex functions, J. Nonl. Funct. Anal., 2017 (2017), 14 pages.
-
[23]
M. A. Noor, K. I. Noor, S. Iftikhar, Integral inequalities for differentiable relative harmonic preinvex functions (survey), TWMS J. Pure Appl. Math., 7 (2016), 3–19.
-
[24]
M. A. Noor, K. I. Noor, S. Iftikhar, M. U. Awan, Strongly generalized harmonic convex functions and integral inequalities, J. Math. Anal., 7 (2016), 66–77.
-
[25]
J. Pecaric, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Acdemic Press, Boston (1992)
-
[26]
B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl., 7 (1966), 72–75.