BibTex RIS Kaynak Göster

generalizations of the Feng Qi Type Inequality for Pseudo-Integral

Yıl 2015, Cilt: 28 Sayı: 4, 695 - 702, 16.12.2015

Öz

In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved. There are considered two cases of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function $g$ (then the pseudo-integrals reduces $g$-integral), and the second with a semiring $([a, b],\max,\odot)$, where the pseudo-multiplication $\odot$ is generated.

Kaynakça

  • bibitem{ham}
  • H. Agahi, M. A. Yaghoobi, A Feng Qi type inequality for Sugeno integral, Fuzzy Inf. Eng. (2010) 3: 293-304.
  • bibitem{Ana}
  • G. Anastassiou, Chebyshev-Gr$overset{..}u$ss type inequalities via Euler type and Fink identities, Mathematics Computing and Modelling 45 (2007) 1189-1200.
  • bibitem{bou}
  • L. Bougoffa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics 7(2) (2006) article 60.
  • bibitem{cab}
  • J. Caballero, K. Sadarangani, Hermite-Hadamard inequality for fuzzy integrals. Applied Mathematics and Computation
  • (2009) 2134-2138.
  • bibitem{che}
  • T. Y. Chen, H. L. Chang, G. H. Tzeng, Using fuzzy measures and habitual domains to analyze the public attitude and apply to the gas taxi policy, European Journal of Operational Research 137 (2002) 145-161.
  • bibitem{Dar}
  • B. Daraby, Generalization of the Stolarsky type
  • inequality for pseudo-integrals, Fuzzy Sets and Systems 194 (2012) 90-96.
  • bibitem{dar}
  • B. Daraby, L. Arabi, Related Fritz Carlson type inequality for Sugeno integrals, Soft Computing 17 (2013) 1745-1750.
  • bibitem{flo}
  • A. Flores-Franuli$check{c}$, H. Rom$acute{a}$n-Flores, A Chebyshev type inequality for fuzzy integrals, Applied Mathematics and Computation 190 (2007) 1178-1184.
  • bibitem{flor}
  • A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, A convolution type inequality for fuzzy integrals, Applied Mathematics and Computation 195 (2008) 94-99.
  • bibitem{Flo}
  • A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, Markov type inequalities
  • for fuzzy integrals, Applied Mathematics and Computation 207 (2009) 242-247.
  • bibitem{Flor}
  • A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 196 (2008) 55-59.
  • bibitem{hon}
  • D. H. Hong, A sharp Hardy-type inequality of Sugeno integrals, Applied Mathematics and Computation 217 (2010) 437-440.
  • bibitem{kra}
  • S. G. Krantz, Jensen's Inequality, $sharp$ 9.1.3 in Handbook of Complex Variables, Boston, MA: Birkh$overset{..}a$user, 119, 1999.
  • bibitem{luj}
  • J.-Y. Lu , K.-S. Wu, J.-C. Lin, Fast full search in motion estimation by hierarchical use of Minkowski's
  • inequality, Pattern Recognition 31 (1998) 945-952.
  • bibitem{mes1}
  • R. Mesiar, E. Pap, Idempotent integral as limit of $g-$integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
  • bibitem{mes}
  • R. Mesiar, Y. Ouyang, General Chebyshev type inequalities for Sugeno integrals, Fuzzy Sets and Systems 160 (2009) 58-64.
  • bibitem{Mes}
  • R. Mesiar, E. Pap, Idempotent integral as limit of $g$-integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
  • bibitem{min}
  • H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1910.
  • bibitem{ozk}
  • U. M, $overset{..}O$zkan, M. Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Applied
  • Mathematics Letters 21 (2008) 993-1000.
  • bibitem{Pap6}
  • E. Pap, An integral generated by decomposable measure, Univ. Novom
  • Sadu Zb. Rad. Prirod. -Mat. Fak. Ser. Mat. 20 (1) (1990)
  • -144.
  • bibitem{feng}
  • F. Qi, Several integral inequalities. J. Inequal. Pure Appl. Math. 1(2) Art 19.
  • bibitem{wan}
  • Z. Wang, G. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
Yıl 2015, Cilt: 28 Sayı: 4, 695 - 702, 16.12.2015

Öz

Kaynakça

  • bibitem{ham}
  • H. Agahi, M. A. Yaghoobi, A Feng Qi type inequality for Sugeno integral, Fuzzy Inf. Eng. (2010) 3: 293-304.
  • bibitem{Ana}
  • G. Anastassiou, Chebyshev-Gr$overset{..}u$ss type inequalities via Euler type and Fink identities, Mathematics Computing and Modelling 45 (2007) 1189-1200.
  • bibitem{bou}
  • L. Bougoffa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics 7(2) (2006) article 60.
  • bibitem{cab}
  • J. Caballero, K. Sadarangani, Hermite-Hadamard inequality for fuzzy integrals. Applied Mathematics and Computation
  • (2009) 2134-2138.
  • bibitem{che}
  • T. Y. Chen, H. L. Chang, G. H. Tzeng, Using fuzzy measures and habitual domains to analyze the public attitude and apply to the gas taxi policy, European Journal of Operational Research 137 (2002) 145-161.
  • bibitem{Dar}
  • B. Daraby, Generalization of the Stolarsky type
  • inequality for pseudo-integrals, Fuzzy Sets and Systems 194 (2012) 90-96.
  • bibitem{dar}
  • B. Daraby, L. Arabi, Related Fritz Carlson type inequality for Sugeno integrals, Soft Computing 17 (2013) 1745-1750.
  • bibitem{flo}
  • A. Flores-Franuli$check{c}$, H. Rom$acute{a}$n-Flores, A Chebyshev type inequality for fuzzy integrals, Applied Mathematics and Computation 190 (2007) 1178-1184.
  • bibitem{flor}
  • A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, A convolution type inequality for fuzzy integrals, Applied Mathematics and Computation 195 (2008) 94-99.
  • bibitem{Flo}
  • A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, Markov type inequalities
  • for fuzzy integrals, Applied Mathematics and Computation 207 (2009) 242-247.
  • bibitem{Flor}
  • A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 196 (2008) 55-59.
  • bibitem{hon}
  • D. H. Hong, A sharp Hardy-type inequality of Sugeno integrals, Applied Mathematics and Computation 217 (2010) 437-440.
  • bibitem{kra}
  • S. G. Krantz, Jensen's Inequality, $sharp$ 9.1.3 in Handbook of Complex Variables, Boston, MA: Birkh$overset{..}a$user, 119, 1999.
  • bibitem{luj}
  • J.-Y. Lu , K.-S. Wu, J.-C. Lin, Fast full search in motion estimation by hierarchical use of Minkowski's
  • inequality, Pattern Recognition 31 (1998) 945-952.
  • bibitem{mes1}
  • R. Mesiar, E. Pap, Idempotent integral as limit of $g-$integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
  • bibitem{mes}
  • R. Mesiar, Y. Ouyang, General Chebyshev type inequalities for Sugeno integrals, Fuzzy Sets and Systems 160 (2009) 58-64.
  • bibitem{Mes}
  • R. Mesiar, E. Pap, Idempotent integral as limit of $g$-integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
  • bibitem{min}
  • H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1910.
  • bibitem{ozk}
  • U. M, $overset{..}O$zkan, M. Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Applied
  • Mathematics Letters 21 (2008) 993-1000.
  • bibitem{Pap6}
  • E. Pap, An integral generated by decomposable measure, Univ. Novom
  • Sadu Zb. Rad. Prirod. -Mat. Fak. Ser. Mat. 20 (1) (1990)
  • -144.
  • bibitem{feng}
  • F. Qi, Several integral inequalities. J. Inequal. Pure Appl. Math. 1(2) Art 19.
  • bibitem{wan}
  • Z. Wang, G. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
Toplam 51 adet kaynakça vardır.

Ayrıntılar

Bölüm Mathematics
Yazarlar

Bayaz Daraby

Amir Shafiloo Bu kişi benim

Asghar Rahimi Bu kişi benim

Yayımlanma Tarihi 16 Aralık 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 28 Sayı: 4

Kaynak Göster

APA Daraby, B., Shafiloo, A., & Rahimi, A. (2015). generalizations of the Feng Qi Type Inequality for Pseudo-Integral. Gazi University Journal of Science, 28(4), 695-702.
AMA Daraby B, Shafiloo A, Rahimi A. generalizations of the Feng Qi Type Inequality for Pseudo-Integral. Gazi University Journal of Science. Aralık 2015;28(4):695-702.
Chicago Daraby, Bayaz, Amir Shafiloo, ve Asghar Rahimi. “Generalizations of the Feng Qi Type Inequality for Pseudo-Integral”. Gazi University Journal of Science 28, sy. 4 (Aralık 2015): 695-702.
EndNote Daraby B, Shafiloo A, Rahimi A (01 Aralık 2015) generalizations of the Feng Qi Type Inequality for Pseudo-Integral. Gazi University Journal of Science 28 4 695–702.
IEEE B. Daraby, A. Shafiloo, ve A. Rahimi, “generalizations of the Feng Qi Type Inequality for Pseudo-Integral”, Gazi University Journal of Science, c. 28, sy. 4, ss. 695–702, 2015.
ISNAD Daraby, Bayaz vd. “Generalizations of the Feng Qi Type Inequality for Pseudo-Integral”. Gazi University Journal of Science 28/4 (Aralık 2015), 695-702.
JAMA Daraby B, Shafiloo A, Rahimi A. generalizations of the Feng Qi Type Inequality for Pseudo-Integral. Gazi University Journal of Science. 2015;28:695–702.
MLA Daraby, Bayaz vd. “Generalizations of the Feng Qi Type Inequality for Pseudo-Integral”. Gazi University Journal of Science, c. 28, sy. 4, 2015, ss. 695-02.
Vancouver Daraby B, Shafiloo A, Rahimi A. generalizations of the Feng Qi Type Inequality for Pseudo-Integral. Gazi University Journal of Science. 2015;28(4):695-702.