We prove a common fixed point result for $(f,g)$-nonexpansive maps and then derive certain results on best approximation. Our results generalize the results of Al-Thagafi [1], Jungck and Sessa [6], Khan, Hussain and Thaheem [8], Latif [9, 10] and Sahab, Khan and Sessa [12].

Emulsions stand among the most important multiphase fluids, exhibiting various complicated phenomenon. To understand the process of emulsification, the Taylor equation has been extended to incorporate the parameters that depend on molecular mass of oil and their contents and the amount of surfactant added. To test the validity of the proposed equations, four well-defined short chain (n-hexane, n-heptane, n-decane, and kerosene) oils were emulsified in water and the results were compared with the experimental ones. It has been concluded that the extended Taylor equation worked well, even in the presence of surfactant. The quality of the emulsion defined and discussed in terms of size and number of droplets was best near CMC of the surfactant used. A relationship has also been derived between CMC of surfactant and its distribution coefficient, which allows the exact value of one parameter to be determined if other is known.

A nylon 6 sample having average molecular mass 4.825 Â 10 5 g mol À1 was fractionated into five different fractions with respect to molecular mass, which ranged from 3691 to 999,000 g mol À1 . The light scattering and intrinsic viscosity measurements were made in m-cresol and its mixture with 1,4-dioxane. The second virial coefficient, radius of gyration and Mark Houwink's constant and unperturbed chain dimensions were determined by light scattering and viscosity measurement. It has been observed that all these parameters are composition of solvent and temperature dependent. The solvent having composition of 97% m-cresol and 3% dioxane, was best and it deteriorated with the increase/decrease in percentage of 1,4-dioxane in m-cresol. However, its thermodynamic quality was enhanced with the temperature. Such variation in quality of solvent was reflected in all the estimated parameters and showed maxima at this composition of solvent. The unperturbed dimensions obtained by different methods though, differed in values but showed same trend and NA-MKB method gave close results to the one obtained through [g o ]. A new expression has also been proposed relating k o to solvent quality and temperature and the data obtained by us for nylon-6 and the one obtained from the literature for dextran obeyed this expression up to large extent irrespective of the solvent composition and temperature. The proposed equations have also been applied to dextran/methoxy ethylene and dextran/ethylene glycol systems and worked well.

<abstract><p>The purpose of this paper is to present a new concept of a Banach algebra in a fuzzy metric space (FM-space). We define an open ball, an open set and prove that every open ball in an FM-space over a Banach algebra $ \mathcal{A} $ is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over $ \mathcal{A} $. Moreover, we state and prove a fuzzy Banach contraction theorem on FM-spaces over a Banach algebra $ \mathcal{A} $. Furthermore, we present an application of an integral equation and will prove a result dealing with the integral operators in FM-spaces over a Banach algebra.</p></abstract>

Abstract. In this paper, we present a generalization of some fixed point and coincidence point theorems using the notion of a w − distance on a complete metric space. Consequently, we improve and generalize various results existing in the literature.