본문 바로가기
KERD
논문KCI 등재

On harmonic (h,r)-convex functions

Khalida Inayat Noor|SABAH IFTIKHAR|Muhammad Aslam Noor
장전수학회 (Jangjeon Mathematical Society)|2018.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제21권 제2호|pp. 239-251|DOI 10.17777/pjms.2018.21.2.008

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Harmonic convex functionsHermite-Hadamard type inequalityr-convex functionsh-convex functions(hr)- convex function
주제분류수학

초록

In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary nonnegative function h, which is called harmonic (h, r)-convex functions. We establish some new Hermite- Hadamard integral inequalities for this new class of harmonic (h, r)- convex functions. Our results represent a significant refinement of the known and new special cases. Ideas an techniques of this paper may motivate further research in this dynamic field.

Abstract

In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary nonnegative function h, which is called harmonic (h, r)-convex functions. We establish some new Hermite- Hadamard integral inequalities for this new class of harmonic (h, r)- convex functions. Our results represent a significant refinement of the known and new special cases. Ideas an techniques of this paper may motivate further research in this dynamic field.

참고문헌 (30)

  1. G. D. Anderson, "Generalized convexity and inequalities", J. Math. Anal. Appl., 335, pp.1294~1308 (2007)[DOI]
  2. M. Alomari, "New inequalities of Simpson's type for s-convex functions with applications", RGMIA Res. Rep. Coll, 12(4) (2009)
  3. W. W. Breckner, "Stetigkeitsaussagen fur eine Klass verallgemeinerter Konvex funktionen in topologischen linearen Raumen", Publ. lnst. Math., 23, pp.13~20 (1978)
  4. G. Cristescu, "Non-connected Convexities and Applications" (2002), Kluwer Academic Publisher
  5. G. Cristescu, "Improved integral inequalities for product of convex functions", J. Inequal. Pure Appl. Math., 6(2), pp.35~ (2005)
  6. S.S. Dragomir, "Inequalities of Hermite-Hadamard type for HA-convex functions", RGMIA Res. Rep. Coli., 18 (2015)
  7. E. K. Godunova, "Neravenstva dlja funkcii sirokogo klassa soderzascego vypuklye monotonnye i nekotorye drugie vidy funkii. Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nanc. MGPI Moskva", pp.138~142 (1985)
  8. C. Hermite, "Sur deux limites d'une intgrale dfinie", Mathesis, 3, pp.82~ (1883)
  9. J. Hadamard, "Etude sur les proprietes des fonctions entieres e.t en particulier dune function consideree par Riemann", J. Math. Pure Appl., 58, pp.171~215 (1893)
  10. L. V. Hap, "On some Hadamard-type inequalities for (h, r)-convex functions", Int. J. Math. Anal., 7(42), pp.2067~2075 (2013)[DOI]
  11. I, Iscan, "Hermite-Hadamard type inequalities for harmonically convex functions", Hacett, J. Math. Stats., 43(6), pp.935~942 (2014)
  12. N. P. N. Ngoc, "Integral inequalities of Hadamard type for r-Convex functions", Int. Math. Forum, 4(35), pp.1723~1728 (2009)
  13. C. P. Niculescu, "Convex Functions and Their Applications" (2006), Springer-Verlag
  14. M. A. Noor, "Advanced Numerical Analysis, Letcure Notes" (2017)
  15. M. A. Noor, "General variational inequalities", Appl. Math. Letters, 1, pp.119~121 (1988)[DOI]
  16. M. A. Noor, "Some dvelopment in general variational inequalities", Appl. Math. Comput., 251, pp.199~277
  17. M. A. Noor, "Extended general variational inequalities", Appl. Math. Letters, 22(2), pp.182~186 (2009)[DOI]
  18. M. A. Noor, "Haromnic variational inequalities", Appl. Math. Inform. Sci., 10(5), pp.1811~1814 (2016)[DOI]
  19. M. A. Noor, "Some implicit methods for solving harmonic variational inequalites", Inter. J. Anal. Appl., 12(1), pp.10~14 (2016)
  20. M. A. Noor, "Some new estimates of Hermite-Hadamard inequalities via harmonically r-convex functions", Le Matemat, 71(2), pp.117~127 (2016)
  21. M. A. Noor, "Some integral inequalities for harmonically h-convex functions", U.P.B. Sci. Bull. Serai A, 77(1), pp.5~16 (2015)
  22. M. A. Noor, "Some characterizations of harmonic convex functions", Inter. J. Anal. Appl., 15(2), pp.179~187 (2017)
  23. J. Park, "On the Hermite-Hadamard-like type inequalities for co-ordinated (s, r)- convex mappings", Int. J. Pure Appl. Math., 74(2), pp.251~263 (2012)
  24. C.E.M. Pearce, "On Weighted Generalized Logarithmic Means", Houston .J. Math., 24(3), pp.459~ (1998)
  25. J. Pecaric, "Convex Functions, Partial Orderings and Statistical Applications" (1992), Acdemic Press
  26. M. Z. Sarikaya, "On the Hadamard type integral inequalities involving several differentiable <TEX>$\phi$<", TEX>-r-convex functions, 2012
  27. H. N. Shi, "Some new judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions", J. Inequal. Appl., 527 (2013)
  28. M. Tunc, "On some new inequalities for convex functions", Turk. J. Math., 36, pp.245~251 (2012)
  29. S. Varosanec, "On h-convexity", J. Math. Anal. Appl., 326, pp.303~311 (2007)[DOI]
  30. G. S. Yang, "Refinements of Hadamards inequality for r-convex functions", Indian J. Pure Appl. Math, 32(10), pp.1571~1579 (2001)

관련 논문AI추천

Fractional integral inequalities for harmonic geometrically h-convex functionsKhalida Inayat Noor, Muhammad Aslam Noor, SABAH IFTIKHAR장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호INEQUALITIES FOR COORDINATED HARMONIC PREINVEX FUNCTIONSKhalida Inayat Noor, MUHAMMAD ASLAM NOOR, SABAH IFTIKHAR, Themistocles M. Rassias장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functionsAI-PING JI, Feng Qi, TIAN-YU ZHANG장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2013 · 제16권 제3호Hermite-Hadamard-Fejer Type Inequalities for Harmonically Quasi-convex Functions via Fractional IntegralsImdat Iscan, Mehmet Kunt경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호SOME INEQUALITIES FOR GEOMETRICALLY PREINVEX FUNCTIONSKhalida Inayat Noor, Muhammad Aslam Noor, SUNDAS KHAN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제1호Fractional integral inequalities of Hermite-Hadamard type for m-HH convex functions with applicationsHui Zhou, Imdat Iscan, Wen Wang장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호

이 간행물의 다른 논문 (12건)

GENERAL STRUCTURE OF TWO-DIMENSIONAL QUASIREPRESENTATIONS OF GROUPSA. I. Shternpp. 167-170Congruences modulo 7 and 11 for (s,t)-regular bipartitionsRanganatha D.pp. 171-183On the asymptotic deficiency of some statistical estimators based on samples with random sizeBening V.E.pp. 185-193A note on degenerate stirling numbers and their applications김대산, 김태균, 권혁인pp. 195-203DUNKEL TYPE INEQUALITIES INVOLVING HYPERBOLIC FUNCTIONSQIUYAN ZHANG, WAN-LAN WANGpp. 205-219
원문 보기