the purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fixed point on geraghty-contraction. in this paper,denitions of approximate -pair fixed point for two maps tα , sα and theirdiameters are given in a metric space.

Boundary integral methods have been used widely for the simulation of interfacial Stokes flows. These free surface representations reduce the problem to one defined solely on the fluid interface. Often the assumption of axi-symmetry is used to further reduce the dimensionality of the problem. However, it is difficult to obtain high order approximations to the resulting line integrals due to the...

Boundary integral equations and Nyström discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weaklysingular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarith...

In many applications of ageand size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Si...

Abstract We observe that every quadrature of numerical integration together with a strictly increasing and continuous function generates mean then we study this family means. characterize the functions which generate weighted arithmetic means in way show how to obtain comparison type theorems for generated by different quadratures.