HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS

Abdullah Akkurt; Hüseyin Yıldırım

Araştırma Makalesi

Yıl 2021, Cilt: 4 Sayı: 1, 87 - 101, 31.01.2021

Abdullah Akkurt Hüseyin Yıldırım

Öz

Kaynakça

Barani, A.; Ghazanfari, A.G.; Dragomir, S.S.: Hermite-Hadamardinequality for functions whose derivatives absolute values are preinvex. J.Inequal. Appl. 2012, 247 (2012)
Dragomir, S.S.; Pearce, C.E.M.: Selected topics onHermite--Hadamard inequalities and applications. Victoria University (2000)
Dragomir, S.S.; Pecaric, J.; Persson, L.E.: Some inequalities ofHadamard type. Soochow J. Math. 21, 335--341, (1995)
\.{I}\c{s}can, \.{I}.: Hermite--Hadamard's inequalities forpreinvex function via fractional integrals and related functionalinequalities, Am. J. Math. Anal. 1 (3) (2013) 33--38.
Latif, M.A.: Some inequalities for differentiable prequasiinvexfunctions with applications. Konuralp J. Math. 1(2), 17--29 (2013)
Latif, M.A.; Dragomir, S.S.: Some Hermite-Hadamard typeinequalities for functions whose partial derivatives in absloute value arepreinvex on the co-oordinates. Facta Universitatis (NIS) Ser. Math. Inform.28(3), 257--270, (2013)
Latif, M.A.; Dragomir, S. S.; Momoniat, E.: Some weightedintegral inequalities for differentiable preinvex and prequasiinvexfunctions. RGMIA (2014)
Noor, M.A.: On Hadamard integral inequalities involving twolog-preinvex functions. J. Inequal. Pure Appl. Math. 8, 1--6 (2007)
Noor, M.A.: On Hermite-Hadamard integral inequalities forproduct of two nonconvex functions. J. Adv. Math. Studies 2(1), 53--62 (2009)
Noor, M.A.: Some new classes of nonconvex functions. Nonl.Funct. Anal. Appl. 11(1), 165--171 (2006)
Noor, M.A.; Awan, M.U.; Noor, K.I.: On some inequalities forrelative semi-convex functions. J. Inequal. Appl., 2013, 332 (2013)
Noor, M.A.; Noor, K.I.: Generalized preinvex functions andtheir properties. Journal of Appl. Math. Stochastic Anal., 2006(12736),1--13, doi:10.1155/JAMSA/2006/12736
Noor, M.A.; Noor, K.I.; Ashraf, M.A.; Awan, M.U.; Bashir, B.:Hermite--Hadamard inequalities for $h_{\varphi }-$convex functions. Nonl.Anal. Formum. 18, 65--76 (2013)
Noor, M.A.; Noor, K.I.; Awan, M.U.: Hermite--Hadamardinequalities for relative semi-convex functions and applications. Filomat,28(2), 221--230, (2014)
Noor, M.A.; Noor, K.I.; Awan, M.U.: Generalized convexity andintegral inequalities. Appl. Math. Inf. Sci. 9(1), 233--243, (2015)
Noor, M.A.; Noor, K.I.; Awan, M.U.; Khan, S.: FractionalHermite-Hadamard inequalities for some new classes of Godunova--Levinfunctions. Appl. Math. Inf. Sci. 8(6), 2865--2872, (2014)
Noor, M.A.; Noor, K.I.; Awan, M.U.; Li, J.: OnHermite--Hadamard type Inequalities for h-preinvex functions, Filomat 28:7(2014), 1463--1474, DOI 10.2298/FIL1407463N
Noor, M.A.; Noor, K.I.; Al-Said, E.: Iterative methods forsolving nonconvex equilibrium variational inequalities. Appl. Math. Inf.Sci. 6(1), 65--69, (2012).
Noor, M.A.; Postolache, M.; Noor, K.I.; Awan, M.U.:Geometrically nonconvex functions and integral inequalities. Appl. Math.Inf. Sci. 9, (2015).
Noor, M.A.; Noor, K.I.; Awan, M.A.; Khan, S.: Hermite--Hadamardtype inequalities for differantiable $h_{\varphi }-$preinvex functions.Arab. J. Math.4:63-76 (2015).
Sarikaya, M.Z.; Set, E.: \"{O}zdemir M.E.: On some newinequalities of Hadamard type involving h-convex functions. Acta Math. Univ.Comenianae. 2, 265--272 (2010).
Sarikaya, M.Z.; Alp, N.; Bozkurt, H.: On Hermite-Hadamard TypeIntegral Inequalities for preinvex and log-preinvex functions, ContemporaryAnalysis and Applied Mathematics, Vol.1, No.2, 237-252, 2013.
Varosanec, S.: On h-convexity. J. Math. Anal. Appl. 326,303--311 (2007)
Weir, T.; Mond, B.: Preinvex functions in multiple objectiveoptimization. J. Math. Anal. Appl. 136, 29--38 (1998)
Samko, S.G.; Kilbas, A.A.; Marichev, O.I.: Fractional Integralsand Derivatives, Theory and Applications, Gordon and Breach, Yverdon,Switzerland, 1993

HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS

Yıl 2021, Cilt: 4 Sayı: 1, 87 - 101, 31.01.2021

Abdullah Akkurt Hüseyin Yıldırım

Öz

In this paper, we consider a new class of convex functions which is called h_varphi-preinvex functions. We prove several Hermite--Hadamard type

inequalities for differentiable h_varphi-preinvex functions via Fractional Integrals. Some special cases are also discussed. Our results

extend and improve the corresponding ones in the literature.

Anahtar Kelimeler

integral inequalities, fractional integrals, Hermite-Hadamard Inequality

Kaynakça

Barani, A.; Ghazanfari, A.G.; Dragomir, S.S.: Hermite-Hadamardinequality for functions whose derivatives absolute values are preinvex. J.Inequal. Appl. 2012, 247 (2012)
Dragomir, S.S.; Pearce, C.E.M.: Selected topics onHermite--Hadamard inequalities and applications. Victoria University (2000)
Dragomir, S.S.; Pecaric, J.; Persson, L.E.: Some inequalities ofHadamard type. Soochow J. Math. 21, 335--341, (1995)
\.{I}\c{s}can, \.{I}.: Hermite--Hadamard's inequalities forpreinvex function via fractional integrals and related functionalinequalities, Am. J. Math. Anal. 1 (3) (2013) 33--38.
Latif, M.A.: Some inequalities for differentiable prequasiinvexfunctions with applications. Konuralp J. Math. 1(2), 17--29 (2013)
Latif, M.A.; Dragomir, S.S.: Some Hermite-Hadamard typeinequalities for functions whose partial derivatives in absloute value arepreinvex on the co-oordinates. Facta Universitatis (NIS) Ser. Math. Inform.28(3), 257--270, (2013)
Latif, M.A.; Dragomir, S. S.; Momoniat, E.: Some weightedintegral inequalities for differentiable preinvex and prequasiinvexfunctions. RGMIA (2014)
Noor, M.A.: On Hadamard integral inequalities involving twolog-preinvex functions. J. Inequal. Pure Appl. Math. 8, 1--6 (2007)
Noor, M.A.: On Hermite-Hadamard integral inequalities forproduct of two nonconvex functions. J. Adv. Math. Studies 2(1), 53--62 (2009)
Noor, M.A.: Some new classes of nonconvex functions. Nonl.Funct. Anal. Appl. 11(1), 165--171 (2006)
Noor, M.A.; Awan, M.U.; Noor, K.I.: On some inequalities forrelative semi-convex functions. J. Inequal. Appl., 2013, 332 (2013)
Noor, M.A.; Noor, K.I.: Generalized preinvex functions andtheir properties. Journal of Appl. Math. Stochastic Anal., 2006(12736),1--13, doi:10.1155/JAMSA/2006/12736
Noor, M.A.; Noor, K.I.; Ashraf, M.A.; Awan, M.U.; Bashir, B.:Hermite--Hadamard inequalities for $h_{\varphi }-$convex functions. Nonl.Anal. Formum. 18, 65--76 (2013)
Noor, M.A.; Noor, K.I.; Awan, M.U.: Hermite--Hadamardinequalities for relative semi-convex functions and applications. Filomat,28(2), 221--230, (2014)
Noor, M.A.; Noor, K.I.; Awan, M.U.: Generalized convexity andintegral inequalities. Appl. Math. Inf. Sci. 9(1), 233--243, (2015)
Noor, M.A.; Noor, K.I.; Awan, M.U.; Khan, S.: FractionalHermite-Hadamard inequalities for some new classes of Godunova--Levinfunctions. Appl. Math. Inf. Sci. 8(6), 2865--2872, (2014)
Noor, M.A.; Noor, K.I.; Awan, M.U.; Li, J.: OnHermite--Hadamard type Inequalities for h-preinvex functions, Filomat 28:7(2014), 1463--1474, DOI 10.2298/FIL1407463N
Noor, M.A.; Noor, K.I.; Al-Said, E.: Iterative methods forsolving nonconvex equilibrium variational inequalities. Appl. Math. Inf.Sci. 6(1), 65--69, (2012).
Noor, M.A.; Postolache, M.; Noor, K.I.; Awan, M.U.:Geometrically nonconvex functions and integral inequalities. Appl. Math.Inf. Sci. 9, (2015).
Noor, M.A.; Noor, K.I.; Awan, M.A.; Khan, S.: Hermite--Hadamardtype inequalities for differantiable $h_{\varphi }-$preinvex functions.Arab. J. Math.4:63-76 (2015).
Sarikaya, M.Z.; Set, E.: \"{O}zdemir M.E.: On some newinequalities of Hadamard type involving h-convex functions. Acta Math. Univ.Comenianae. 2, 265--272 (2010).
Sarikaya, M.Z.; Alp, N.; Bozkurt, H.: On Hermite-Hadamard TypeIntegral Inequalities for preinvex and log-preinvex functions, ContemporaryAnalysis and Applied Mathematics, Vol.1, No.2, 237-252, 2013.
Varosanec, S.: On h-convexity. J. Math. Anal. Appl. 326,303--311 (2007)
Weir, T.; Mond, B.: Preinvex functions in multiple objectiveoptimization. J. Math. Anal. Appl. 136, 29--38 (1998)
Samko, S.G.; Kilbas, A.A.; Marichev, O.I.: Fractional Integralsand Derivatives, Theory and Applications, Gordon and Breach, Yverdon,Switzerland, 1993

Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Araştırma Makalesi
Yazarlar	Abdullah Akkurt 0000-0001-5644-1276 Hüseyin Yıldırım
Yayımlanma Tarihi	31 Ocak 2021
Gönderilme Tarihi	6 Eylül 2019
Kabul Tarihi	27 Şubat 2020
Yayımlandığı Sayı	Yıl 2021 Cilt: 4 Sayı: 1

Kaynak Göster

APA	Akkurt, A., & Yıldırım, H. (2021). HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS. Journal of Universal Mathematics, 4(1), 87-101.
AMA	Akkurt A, Yıldırım H. HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS. JUM. Ocak 2021;4(1):87-101.
Chicago	Akkurt, Abdullah, ve Hüseyin Yıldırım. “HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 4, sy. 1 (Ocak 2021): 87-101.
EndNote	Akkurt A, Yıldırım H (01 Ocak 2021) HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS. Journal of Universal Mathematics 4 1 87–101.
IEEE	A. Akkurt ve H. Yıldırım, “HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS”, JUM, c. 4, sy. 1, ss. 87–101, 2021.
ISNAD	Akkurt, Abdullah - Yıldırım, Hüseyin. “HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 4/1 (Ocak 2021), 87-101.
JAMA	Akkurt A, Yıldırım H. HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS. JUM. 2021;4:87–101.
MLA	Akkurt, Abdullah ve Hüseyin Yıldırım. “HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS”. Journal of Universal Mathematics, c. 4, sy. 1, 2021, ss. 87-101.
Vancouver	Akkurt A, Yıldırım H. HERMITE--HADAMARD TYPE INEQUALITIES VIA DIFFERENTIABLE hφ−h_{\varphi }-hφ− PREINVEX FUNCTIONS FOR FRACTIONAL INTEGRALS. JUM. 2021;4(1):87-101.

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