FRACTIONAL OSTROWSKI INEQUALITIES FOR HARMONIC h-PREINVEX FUNCTIONS

Muhammad Aslam Noor, Khalida Inayat Noor, Sabah Iftikhar

DOI Number
-
First page
417
Last page
445

Abstract


 In this  paper, we introduce a new class of harmonic preinvex  functions, which is called harmonic h−preinvex functions. Several  new Ostrowski type inequal- ities for harmonic h -preinvex  functions via Riemann-Liouville fractional integrals are established.  Some special  cases  are  also discussed,  which  appers  to  be a new ones. Results obtained in this  paper  continue to  hold  for these  cases.   Interested readers are  encouraged to  find the  applications of these  harmonic h−  preinvex  functions in pure  and  applied  sciences.

 


Keywords

Harmonic convex functions, preinvex functions, harmonic preinvex func- tions, h-convex functions, Ostrowski-type inequality

Keywords


Harmonic convex functions, preinvex functions, Harmonic preinvex func- tions, h -convex functions, Ostrowski type inequality.

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References


M. Alomari, M. Darus, S. S. Dragomir, and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett.

(1)(2010), 1071-1076.

G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen. Generalized convexity and inequalities. J. Math. Anal. Appl., 335(2007), 1294-1308.

M. W. Alomari, M. Darus, and U. S. Kirmaci, Some inequalities of Hermite- Hadamard type for s-convex functions, Acta Math. Sci. B31, 4(2011), 16431652.

M. Avci, H. Kavurmaci and M. Emin Ozdemir, New inequalities of Hermite- Hadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput. 217(2011), 51715176.

W. W. Breckner, Stetigkeitsaussagen fur eine Klass verallgemeinerter Konvex funk- tionen in topologischen linearen Raumen, Publ. Inst. Math., 23(1978), 13-20 .

A. Barani, A. G. Ghazanfari and S. S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl., 2012,

(2012).

A. Ben-Isreal and B. Mond. What is invexity? J. Austral. Math. Soc., Ser. B,

(1986), No 1, 1-9.

S. S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose second derivative are bounded and applications, RGMIA Res. Rep. Coll,

(2)(1998), Art 9.

S.S. Dragomir, S. Fitzpatrick, The Hadamards inequality for s-convex functions in the second sense, Demonstratio Math. 32(4) (1999), 687696.

S. S. Dragomir, J. Peccaric and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21(1995), 335-341.

E. K. Godunova and V. I. Levin, Neravenstva dlja funkcii sirokogo klassa soderza- scego vypuklye monotonnye i nekotorye drugie vidy funkii. Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. MGPI Moskva. (1985), 138-142, in Russia.

C. Hermite, Sur deux limites d’une intgrale dfinie. Mathesis, 3(1883), 82.

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.

S. Hussain, M. I. Bhatti, and M. Iqbal, Hadamard-type inequalities for s-convex functions I, J. Math., Punjab Univ., 41(2009), 5160.

H. Hudzik , L. Maligranda, Some remarks on s-convex functions, Aequationes

Math., 48 (1994), 100111.

M. A. Hanson. On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl.,

(1981), 545-550.

Iscan, New estimates on generalization of some integral inequalities for s-convex functions and their applications,Int. J. Pure Appl. Math., 86(4)(2013), 727-746.

I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43(6)(2014), 935-942.

I. Iscan, Generalization of different type integral inequalities for s-convex functions via fractional integrals. Appl. Anal., 93(9)(2014), 1846-1862.

I. Iscan, Generalization of different type integral inequalities via fractional integrals for functions whose second derivatives absolute values are quasi-convex. Konuralp J. Math., 1(2)(2013), 6779.

I. Iscan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals, J. Inequal. Appl., 2013; (491)(2013), 1-15.

I. Iscan, Ostrowski type inequalities for harmonically s -convex functions, Konuralp.

J. Math., 3(1)(2015), 63-74.

I. Iscan and S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238(2014), 237-244.

I. Iscan, Ostrowski type inequalities for harmonically s -convex functions via frac- tional integrals, arXiv: 1313. 7666v2 [math. CA], (2013).

M. A. Latif, Some inequalities for differentiable prequasiinvex functions with ap- plications, Konuralp J. Math., 1(2)(2013), 1729.

M. A. Latif and S. S. Dragomir, Some Hermite-Hadamard type inequalities for func- tions whose partial derivatives in absloute value are preinvex on the co-oordinates, Facta Universitatis (NIS) Ser. Math. Inform., 28(3)(2013), 257270.

M. A. Latif, S. S. Dragomir and E. Momoniat, Some weighted integral inequalities for differentiable preinvex and prequasiinvex functions, RGMIA (2014).

C. P. Niculescu and L. E. Persson. Convex Functions and Their Applications.

Springer-Verlag, New York, (2006).

M. A. Noor, Variational-like inequalities, Optimization, 30(1994), 323-330.

M. A. Noor. Invex equilibrium problems, J. Math. Anal. Apppl., 302(2005), 463-

M. A. Noor and K. I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Apppl., 316(2006), 697-706.

M. A. Noor, Hermite-Hadamard integral inequalities for log-preinvex functions, J.

Math. Anal. Approx. Theory, 2(2007), 126-131.

M. A. Noor, K. I. Noor, M. U. Awan and S. Costache, Some integral inequalities for harmonically h-convex functions, U.P.B. Sci. Bull. Serai A, 77(1)(2015), 5-16.

M. A. Noor, K. I. Noor and M. U. Awan, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Equat., 60(6)(2015), 776-

M. A. Noor, K. I. Noor and M. U. Awan. Integral inequalities for harmonically s-Godunova-Levin functions. FACTA Universitatis(NIS)-series Mathematics and Informatic 29(4)(2014), 415-424.

M. A. Noor, K. I. Noor, M. U. Awan and Jueyou Li, On Hermite-Hadamard inequalities for h-preinvex functions, Filomat 28(7)(2014), 14631474, DOI

2298/FIL1407463N.

M. V. Mihai. M. A. Noor, K. I. Noor and M. U. Awan, Some integral inequalities for harmonically h-convex functions involving hypergeometric functions, Appl. Math. Comput., (252)(2015), 257-262. DOI: 10.1016/j.amc.2014.12.018.

M. A. Noor, K. I. Noor and M. U. Awan, Hermite-Hadamard inequalities for s- Godunova-Levin preinvex functions, J. Adv. Math. Stud., 7(2)(2014), 12-19.

M. A. Noor, K. I. Noor and S. Iftikhar, Nonconvex functions and integral inequal- ities, Punj. Univ. J. Math. 47(2)(2015).

M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for harmonic preinvex functions, Preprint, (2015).

M. A. Noor, K. I. Noor and S. Iftikhar, Integral inequalities for differentiable har- monic h-preinvex functions, Preprint, (2015).

J. Pecaric, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings, and

Statistical Applications, Acdemic Press, New york, (1992).

A. Pitea, M. Postolache, Duality theorems for a new class of multitime multiobjec- tive variational problems, J. Glob. Optim. 54(1)(2012), 4758.

A. Pitea, M. Postolache, Minimization of vectors of curvilinear functionals on the second order jet bundle, Optim. Lett., 6(3)(2012), 459470.

A. Pitea, M. Postolache, Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions, Optim. Lett., 6(8)(2012),

S. Varosanec, On h-convexity, J. Math. Anal. Appl., 326(2007), 303-311.

T. Weir, B. Mond, Preinvex functions in multiobjective optimization, J. Math.

Anal. Appl., 136(1988), 29-38.

X. M. Yang and D. Li, On properties of preinvex functions, J. Math. Anal. Appl.,

(2001), 229-241.

H. N. Shi and Zhang. Some new judgement theorems of Schur geometric and

Schur harmonic convexities for a class of symmetric functions. J. Inequal. Appl.,

(2013).


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