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INEQUALITIES VIA STRONGLY p; h -HARMONIC CONVEX FUNCTIONS

Yıl 2020, Cilt: 10 Sayı: 1, 81 - 94, 01.01.2020

Öz

The main aim of this paper is to consider a new class of harmonic convex functions with respect to an arbitrary non-negative function, which is called strongly p; h -harmonic convex function. We establish Hermite-Hadamard like integral inequal- ities via these new classes of convex functions. Some special cases are discussed, which can be obtained from our main results. The ideas and techniques of this paper may stimulate further research.

Kaynakça

  • Anderson, G. D., Vamanamurthy, M. K. and Vuorinen, M., (2007), Generalized convexity and in- equalities, J. Math. Anal. Appl., 335, pp. 1294-1308.
  • Angulo, H., Gimenez, J., Moros, A. M. and Nikodem, K., (2011), On strongly h-convex functions, Ann. Funct. Anal., 2, pp. 87-93.
  • Cristescu G. and Lupsa, L., (2002), Non-connected Convexities and Applications, Kluwer Academic Publisher, Dordrechet, Holland.
  • Hermite, C., (1883), Sur deux limites d’une intgrale dfinie. Mathesis, 3, 82.
  • Hadamard, J., (1893), Etude sur les proprietes des fonctions entieres e.t en particulier dune fonction consideree par Riemann. J. Math. Pure Appl., 58, pp. 171-215.
  • Iscan, I., (2014), Hermite-Hadamard type inequalities for harmonically convex functions. Hacett, J. Math. Stats., 43(6), pp. 935-942.
  • Merentes, N. and Nikodem, K., (2010), Remarks on strongly convex functions, Aequationes Math. 80(1-2), pp. 193-199.
  • Nikodem, K. and Pales, Z., (2011), Characterizations of inner product spaces by strongly convex functions, Banach J. Math. Anal. 5(1), pp. 8387.
  • Niculescu C. P. and Persson, L. E., (2006), Convex Functions and Their Applications, Springer-Verlag, New York.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2015), Nonconvex functions and integral inequalities, Punjab. Uni. J. Math., 47(2), pp. 19-27.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016), Hermite-Hadamard inequalities for harmonic non- convex functions, MAGNT Research Report, 4(1), pp. 24-40.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2017), Integral inequalities for differentiable p-harmonic convex functions, Filomat, 31(20), pp. 6575-6584.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016),Integral inequalities for differentiable relative har- monic preinvex functions(survey), TWMS J. Pure Appl. Math., 7(1), pp. 3-19.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016), Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Inequ. Special Func., 7(3), pp. 99-113.
  • Noor, M. A., Noor, K. I., Iftikhar, S. and Awan, M.U., (2016), Strongly generalized harmonic convex functions and integral inequalities, J. Math. Anal., 7(3), pp. 66-77.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2017), Inequalities via strongly p-harmonic log-convex functions, J. Nonlinear Func. Anal., 2017, Article ID 20.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016), Integral inequalities for extended harmonic convex functions, Advanced Math. Models and Appl. 2(3), pp. 216-229.
  • Pecaric, J., Proschan, F. and Tong, Y. L., (1992), Convex Functions, Partial Orderings and Statistical Applications, Academic Press, New york.
  • Polyak, B.T., (1966), Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7, pp. 7275.
  • Varosanec, S., (2007), On h-convexity, J. Math. Anal. Appl., 326(1), pp. 303-311.
  • Vial, J. P., (1982), Strong convexity of sets and functions, J. Math. Economy, 9, pp. 187205.
Yıl 2020, Cilt: 10 Sayı: 1, 81 - 94, 01.01.2020

Öz

Kaynakça

  • Anderson, G. D., Vamanamurthy, M. K. and Vuorinen, M., (2007), Generalized convexity and in- equalities, J. Math. Anal. Appl., 335, pp. 1294-1308.
  • Angulo, H., Gimenez, J., Moros, A. M. and Nikodem, K., (2011), On strongly h-convex functions, Ann. Funct. Anal., 2, pp. 87-93.
  • Cristescu G. and Lupsa, L., (2002), Non-connected Convexities and Applications, Kluwer Academic Publisher, Dordrechet, Holland.
  • Hermite, C., (1883), Sur deux limites d’une intgrale dfinie. Mathesis, 3, 82.
  • Hadamard, J., (1893), Etude sur les proprietes des fonctions entieres e.t en particulier dune fonction consideree par Riemann. J. Math. Pure Appl., 58, pp. 171-215.
  • Iscan, I., (2014), Hermite-Hadamard type inequalities for harmonically convex functions. Hacett, J. Math. Stats., 43(6), pp. 935-942.
  • Merentes, N. and Nikodem, K., (2010), Remarks on strongly convex functions, Aequationes Math. 80(1-2), pp. 193-199.
  • Nikodem, K. and Pales, Z., (2011), Characterizations of inner product spaces by strongly convex functions, Banach J. Math. Anal. 5(1), pp. 8387.
  • Niculescu C. P. and Persson, L. E., (2006), Convex Functions and Their Applications, Springer-Verlag, New York.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2015), Nonconvex functions and integral inequalities, Punjab. Uni. J. Math., 47(2), pp. 19-27.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016), Hermite-Hadamard inequalities for harmonic non- convex functions, MAGNT Research Report, 4(1), pp. 24-40.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2017), Integral inequalities for differentiable p-harmonic convex functions, Filomat, 31(20), pp. 6575-6584.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016),Integral inequalities for differentiable relative har- monic preinvex functions(survey), TWMS J. Pure Appl. Math., 7(1), pp. 3-19.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016), Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Inequ. Special Func., 7(3), pp. 99-113.
  • Noor, M. A., Noor, K. I., Iftikhar, S. and Awan, M.U., (2016), Strongly generalized harmonic convex functions and integral inequalities, J. Math. Anal., 7(3), pp. 66-77.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2017), Inequalities via strongly p-harmonic log-convex functions, J. Nonlinear Func. Anal., 2017, Article ID 20.
  • Noor, M. A., Noor, K. I. and Iftikhar, S., (2016), Integral inequalities for extended harmonic convex functions, Advanced Math. Models and Appl. 2(3), pp. 216-229.
  • Pecaric, J., Proschan, F. and Tong, Y. L., (1992), Convex Functions, Partial Orderings and Statistical Applications, Academic Press, New york.
  • Polyak, B.T., (1966), Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7, pp. 7275.
  • Varosanec, S., (2007), On h-convexity, J. Math. Anal. Appl., 326(1), pp. 303-311.
  • Vial, J. P., (1982), Strong convexity of sets and functions, J. Math. Economy, 9, pp. 187205.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

M. A. Noor Bu kişi benim

K. I. Noor Bu kişi benim

S. Iftikhar Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

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