jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

Seven new species of Euphranta Loew are described, viz., Euphranta dysoxyli David, sp. nov., E. hyalipennis David & Freidberg, sp. nov, E. diffusa David, sp. nov., E. haldwanica Hancock & Goodger, sp. nov. and E. thandikudi David, sp. nov. from India; E. neochrysopila David, Freidberg, Hancock & Goodger, sp. nov. from Sri Lanka and E. ridleyi Hancock & Goodger, sp. nov. from Singapore. Notes ar...

OBJECTIVES Assessment of the Hardy-Weinberg proportion (HWP) in controls has been widely used as a quality control measure in case-control association studies. However, when the disease being studied is common, controls might not represent the general population, which could result in inaccurate HWP test results. Such results could lead investigators to discard important single-nucleotide polym...

Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ ...