Integral Inequalities for Some New Classes of Convex Functions

Muhammad Aslam Noor; Khalida Inayat Noor; Muhammad Uzair Awan

doi:doi:10.11648/j.ajam.s.2015030301.11

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Integral Inequalities for Some New Classes of Convex Functions

Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan

Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1)

Received: 19 March 2015 Accepted: 21 March 2015 Published: 9 June 2015

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Abstract

In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3-1) This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015)
DOI	10.11648/j.ajam.s.2015030301.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Convex, Hermite-Hadamard’s Inequalities, Convex Functions

References

[1]	W W. Breckner, Stetigkeitsaussagen fiir eine Klasse verallgemeinerter convexer funktionen in topologischen linearen Raumen. Pupl. Inst. Math. 23 (1978), 13-20.
[2]	G.Cristescu and L. Lupsa, Non-connected Convexities and Applications. Kluwer Academic Publishers, Dordrecht, Holland, 2002.
[3]	G. Cristescu, M. A. Noor, M. U. Awan, Bounds of the second degree cumulative frontier gaps of functions with generalized convexity, Carpath. J. Math, 31(2), (2015).
[4]	S. S. Dragomir, Inequalities of Hermite-Hadamard type for -convex functions on linear spaces, preprint, (2014).
[5]	S. S. Dragomir, C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications. Victoria University, Australia, 2000.
[6]	S. S. Dragomir, S. Fitzpatrik, The Hadamard’s inequality for s-convex functions in the second sense, Demonstration Math., 32 (4) (1999), 687–696.
[7]	S. S. Dragomir, J. Pecaric, L. E. Persson, Some inequalities of Hadamard type. Soochow J. Math. 21 (1995), 335-341.
[8]	E. K. Godunova, V. I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii. Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva. (1985) 138-142, (in Russian).
[9]	M. V. Mihai, M. A. Noor, K. I. Noor, M. U. Awan, Some integral inequalities for harmonic h-convex functions involving hypergeometric functions, Appl. Math. Comput. 252 (2015) 257–262.
[10]	M.A. Noor, K.I. Noor, M.U. Awan, Generalized convexity and integral inequalities, Appl. Math. Inf. Sci. 9 (1) (2015), 233–243
[11]	M.A. Noor, K.I. Noor, M.U. Awan, Integral inequalities for coordinated Harmonically convex functions, Complex Var. Elliptic Equ. (2014).
[12]	M.A. Noor, K.I. Noor, M.U. Awan, S. Costache, Some integral inequalities for harmonically h-convex functions, U.P.B. Sci. Bull. Serai A. 77(1) 2015, 5-16.
[13]	M.A. Noor, K.I. Noor, M.U. Awan, S. Khan, Fractional Hermite–Hadamard inequalities for some new classes of Godunova–Levin functions, Appl. Math. Inf. Sci. 8 (6) (2014), 2865–2872.
[14]	M. Z. Sarikaya, A. Saglam, H. Yildirim, On some Hadamard–type inequalities for –convex functions, J. Math. Inequal. 2, 3(2008), 335–341.
[15]	M. Z. Sarikaya, E. Set, M. E. Ozdemir, On some new inequalities of Hadamard type involving -convex functions, Acta Math. Univ. Comenianae LXXIX, 2(2010), 265-272.
[16]	S. Varošanec, On -convexity, J. Math. Anal. Appl. 326 (2007), 303-311.

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APA Style

Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan. (2015). Integral Inequalities for Some New Classes of Convex Functions. American Journal of Applied Mathematics, 3(3-1), 1-5. https://doi.org/10.11648/j.ajam.s.2015030301.11

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ACS Style

Muhammad Aslam Noor; Khalida Inayat Noor; Muhammad Uzair Awan. Integral Inequalities for Some New Classes of Convex Functions. Am. J. Appl. Math. 2015, 3(3-1), 1-5. doi: 10.11648/j.ajam.s.2015030301.11

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AMA Style

Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan. Integral Inequalities for Some New Classes of Convex Functions. Am J Appl Math. 2015;3(3-1):1-5. doi: 10.11648/j.ajam.s.2015030301.11

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@article{10.11648/j.ajam.s.2015030301.11,
  author = {Muhammad Aslam Noor and Khalida Inayat Noor and Muhammad Uzair Awan},
  title = {Integral Inequalities for Some New Classes of Convex Functions},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3-1},
  pages = {1-5},
  doi = {10.11648/j.ajam.s.2015030301.11},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.11},
  abstract = {In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.},
 year = {2015}
}

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TY  - JOUR
T1  - Integral Inequalities for Some New Classes of Convex Functions
AU  - Muhammad Aslam Noor
AU  - Khalida Inayat Noor
AU  - Muhammad Uzair Awan
Y1  - 2015/06/09
PY  - 2015
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DO  - 10.11648/j.ajam.s.2015030301.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
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PB  - Science Publishing Group
SN  - 2330-006X
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AB  - In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.
VL  - 3
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Author Information

Muhammad Aslam Noor

Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
Khalida Inayat Noor

Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
Muhammad Uzair Awan

Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan

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APA Style

Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan. (2015). Integral Inequalities for Some New Classes of Convex Functions. American Journal of Applied Mathematics, 3(3-1), 1-5. https://doi.org/10.11648/j.ajam.s.2015030301.11

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ACS Style

Muhammad Aslam Noor; Khalida Inayat Noor; Muhammad Uzair Awan. Integral Inequalities for Some New Classes of Convex Functions. Am. J. Appl. Math. 2015, 3(3-1), 1-5. doi: 10.11648/j.ajam.s.2015030301.11

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AMA Style

Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan. Integral Inequalities for Some New Classes of Convex Functions. Am J Appl Math. 2015;3(3-1):1-5. doi: 10.11648/j.ajam.s.2015030301.11

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@article{10.11648/j.ajam.s.2015030301.11,
  author = {Muhammad Aslam Noor and Khalida Inayat Noor and Muhammad Uzair Awan},
  title = {Integral Inequalities for Some New Classes of Convex Functions},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3-1},
  pages = {1-5},
  doi = {10.11648/j.ajam.s.2015030301.11},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.11},
  abstract = {In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Integral Inequalities for Some New Classes of Convex Functions
AU  - Muhammad Aslam Noor
AU  - Khalida Inayat Noor
AU  - Muhammad Uzair Awan
Y1  - 2015/06/09
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.11
DO  - 10.11648/j.ajam.s.2015030301.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.11
AB  - In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.
VL  - 3
IS  - 3-1
ER  -

Copy | Download