New Hermite-Hadamard and Jensen Type Inequalities for h-Convex Functions on Fractal Sets
Abstract In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area.
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| Vydáno v: | Revista colombiana de matemáticas Ročník 50; číslo 2; s. 145 - 164 |
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Bogota
Universidad Nacional de Colombia
26.01.2017
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas |
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| ISSN: | 0034-7426, 2357-4100 |
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| Abstract | Abstract In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area. |
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| AbstractList | In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area. Abstract In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area. |
| Author | Hernández, Jorge Merentes, Nelson Vivas, Miguel |
| AuthorAffiliation | Centroccidental Lisandro Alvarado Centroccidental Lisandro Alvarado Barquisimeto Universidad Central de Venezuela |
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| Author_xml | – sequence: 1 givenname: Miguel surname: Vivas fullname: Vivas, Miguel – sequence: 2 givenname: Jorge surname: Hernández fullname: Hernández, Jorge – sequence: 3 givenname: Nelson surname: Merentes fullname: Merentes, Nelson |
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| CitedBy_id | crossref_primary_10_3390_axioms9040117 crossref_primary_10_3390_fractalfract8120728 crossref_primary_10_1002_mma_7081 crossref_primary_10_1002_mma_8680 crossref_primary_10_3390_sym12061034 crossref_primary_10_1016_j_chaos_2023_113172 crossref_primary_10_1186_s13662_020_02865_w crossref_primary_10_4274_BMJ_galenos_2024_2023_6_3 crossref_primary_10_1016_j_chaos_2021_110938 crossref_primary_10_3390_axioms12020106 crossref_primary_10_3390_sym14050840 crossref_primary_10_1016_j_cam_2017_10_007 crossref_primary_10_1016_j_chaos_2019_109547 crossref_primary_10_1186_s13662_020_02812_9 crossref_primary_10_1186_s13662_021_03380_2 |
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| Copyright | Copyright Universidad Nacional de Colombia 2016 This work is licensed under a Creative Commons Attribution 4.0 International License. |
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| DOI | 10.15446/recolma.v50n2.62207 |
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| Keywords | funciones h-convexas desigualdad del tipo Hermite Hadamard h-convex functions convexidad generalizada conjuntos fractales Hermite-Hadamard type inequality Desigualdad del tipo Jensen Jensen inequality Fractal sets generalized convexity |
| Language | English |
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| References | Gounova, E.; Levin, V. 1985; 32 Gounova, E.; Levin, V. 1985; 166 Falconer, K. 1985 Mitrinović, D. S.; Pečarić, J. 1993 Pečarić, J. E.; Proschan, F.; Tong, Y. L. 1992 Mandelbrot, B. B. 1983 Wang, L.; Ma, X.; Liu, L. 2009; 10 Kiliçman, A.; Saleh, W. 2015; 312 Latif, M. A 2010; 4 Simić, S. 2009; 85 Jensen, J. L. W 1906; 32 Noor, M. 2008; 13 Roberts, A. W.; Valberg, D. 1973 Bombardelli, M.; Varošanec, S. 2009; 58 Kirmaci, U. S.; Bakula, M. K.; Özdemir, M. F.; Pečarić, J. 2007; 193 Varošanec, S. 2007; 326 Edgar, G. A. 1990 Bakula, M. Klaričić; Pečarić, J. 2004; 5 Mo, H.; Sui, X. 2014; 28 Breckner, W. W. 1978; 23 Dragomir, S. S. 2015; 32 Yang, X. J. 2012 Mitrinović, D. S.; Lačković, I. B. 1985; 28 Mo, H.; Sui, X.; Yu, D. 2014; 28 Kikianty, Eder Falconer, K. 1990 Kiliçman, A.; Saleh, W. 2015; 301 Pachpatte, B. G. 2003; 6 Merentes, N.; Rivas, S. 2013 Dragomir, S. S.; Fitzpatrick, S. 1999; 32 |
| References_xml | – volume: 32 start-page: 687 year: 1999 end-page: 696 article-title: The hadamard.s inequality for s-convex functions in the second sense publication-title: Demonstratio Math – year: 1985 publication-title: The geometry of fractal sets – volume: 312 year: 2015 article-title: Notions of generalized s-convex functions on fractal sets publication-title: Journal of Inequalities and Applications. Spingeropen Journal – year: 1992 publication-title: Convex functions, partial orderings, and statistical applications – volume: 6 start-page: 119 year: 2003 end-page: 124 article-title: On some inequalities for convex functions publication-title: RGMIA. Res.Rep.Coll.6 Coll – year: 2013 publication-title: El desarrollo del concepto de función convexa, XXVI Escuela venezolana de Matemáticas – volume: 85 start-page: 107 year: 2009 end-page: 110 article-title: On a new converse of jensen's inequality publication-title: Publications de L'Intitut Mathématique. Nouvelle serie – volume: 5 start-page: 119 year: 2004 end-page: 124 article-title: Note of some hadamard type inequality publication-title: Journal of Inequalities in Pure and Applied Mathematics – year: 1993 publication-title: Classical and new inequalities in analysis – volume: 32 start-page: 175 year: 1906 end-page: 193 article-title: Sur les fonctions convexes et le inequalitiés entre les valeurs moyennes publication-title: Acta Math – year: 1990 publication-title: Measure, topology, and fractal geometry – volume: 10 start-page: 6 issue: 2 year: 2009 article-title: A note on some new refinements of jensen's inequality for convex functions publication-title: Journal of Inequalities in Pure and Applied Mathematics – publication-title: Hermite-hadamard inequality in the geometry of banach spaces, Tesis doctoral, School of Engineering and Science Faculty of Health, Engineering and Science Victoria University, 2010 – volume: 58 start-page: 1869 year: 2009 end-page: 1877 article-title: Properties of h-convex functions related to the hermite-hadamard-fejér inequalities publication-title: Computers and Mathematics with Applications – volume: 301 year: 2015 article-title: Some generalizaed hermite-hadamard type integral inequalities for generalized s-convex functions on fractal sets publication-title: Advances in Differences Equations. Spingeropen Journal – volume: 28 start-page: 225 year: 1985 end-page: 232 article-title: Hermite and convexity publication-title: Aequationes Math – year: 1990 publication-title: Fractal geometry – year: 1983 publication-title: The fractal geometry of nature – volume: 326 start-page: 303 year: 2007 end-page: 311 article-title: On h-convexity publication-title: J. Math. Anal. Appl – volume: 28 start-page: 225 year: 2014 end-page: 232 article-title: Generalized convex functions on fractal sets and two related inequalities publication-title: Abstract and Applied Analisys – volume: 23 start-page: 13 year: 1978 end-page: 20 article-title: Stetigkeitsaussagen für eineklasse verallgemeinerter konvexer funktionen in topologischen linearen räumen publication-title: Pub. Inst. Math – volume: 166 start-page: 138 year: 1985 end-page: 142 article-title: Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (russian) numerical mathematics and mathematical physics (russian), Numerical mathematics and mathematical physics (Russian) publication-title: Moskov. Gos. Ped. Inst., Moscow – volume: 32 start-page: 138 year: 1985 end-page: 142 article-title: Neravenstva dlja funkcii širokogo klassa, soderžaščego vypuklye, monotonnye, i nekotorye drugie vidy funkcii, in: Vyčislitel publication-title: Mat. i. Mat. Fiz. Mežvuzov. Sb. Nauč. Trudov. MGPI. Moskva – volume: 4 start-page: 1473 issue: 30 year: 2010 end-page: 1482 article-title: On some inequalities for h-convex functions publication-title: Int. Journal of Math. Analysis – volume: 13 start-page: 119 issue: 2 year: 2008 end-page: 124 article-title: Hermite-hadamard integral inequalities fot log φ-convex functions publication-title: Nonlinear Anaisys Forum – volume: 32 start-page: 323 year: 2015 end-page: 341 article-title: Inequalities of hermite-hadamard type for h-convex functions on linear spaces publication-title: Proyecciones Journal of Mathematics – volume: 193 start-page: 26 year: 2007 end-page: 35 article-title: Hadamard type inequalities for s-convex functions publication-title: Appl. Math. and Comp – volume: 28 start-page: 225 year: 2014 end-page: 232 publication-title: Generalized s-convex functions on fractal sets – year: 1973 publication-title: Convex functions, Pure and Applied Mathematics – year: 2012 publication-title: Advanced local fractional calculus an aplications |
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| Snippet | In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may... Abstract In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may... |
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| SubjectTerms | Convex analysis Inequalities Inequality MATHEMATICS Theoretical mathematics |
| Title | New Hermite-Hadamard and Jensen Type Inequalities for h-Convex Functions on Fractal Sets |
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