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3 results

  • GENERALISATIONS OF INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE THROUGH CONVEXITY

  • Part of
  • MUHAMMAD MUDDASSAR, MUHAMMAD IQBAL BHATTI, WAJEEHA IRSHAD
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 88 / Issue 2 / October 2013
    Published online by Cambridge University Press:
    20 December 2012, pp. 320-330
    Print publication:
    October 2013
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  • In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite–Hadamard integral inequality for mappings whose derivatives are $s$-$(\alpha , m)$-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.

  • HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

  • Part of
  • A. BARANI, S. BARANI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 1 / August 2012
    Published online by Cambridge University Press:
    12 December 2011, pp. 126-134
    Print publication:
    August 2012
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  • In this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

  • THE QUASILINEARITY OF SOME FUNCTIONALS ASSOCIATED WITH THE RIEMANN–STIELTJES INTEGRAL

  • Part of
  • S. S. DRAGOMIR, I. FEDOTOV
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 84 / Issue 1 / August 2011
    Published online by Cambridge University Press:
    05 April 2011, pp. 53-66
    Print publication:
    August 2011
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  • The superadditivity and subadditivity of some functionals associated with the Riemann–Stieltjes integral are established. Applications in connection to Ostrowski’s and the generalized trapezoidal inequalities and for special means are provided.