In this paper, we will ameliorate and generalize Ostrowski type inequality for twice differentiable mappings in various Lebesgue spaces. Some famous inequalities can be derived as a special cases of the inequalities obtained here. Furthermore, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have very rapid applications in numerical integrations and some special means.

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Sm 3+ /Yb 3+ co-doped tellurite glasses are prepared by melt-quenching technique. The density of the glasses varies between 4.65 and 4.84 g/cm 3 . The optical absorption spectra consist of eight bands in the wavelength range of 350-2 000 nm, which correspond to the transitions from ground level 6 H 5/2 to the various excited states of the Sm 3+ ion. Energy band gaps vary in the range of 2.73-2.91 eV, and the Urbach energy ranges from 0.21 to 0.27. Emission spectra exhibit four peaks originating from the 4 G 5/2 energy level centered at 576, 613, 657, and 718 nm. Quenches in emission bands may be due to the energy transfer from the Sm 3+ to Yb 3+ ions.