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In this paper, we study the images of circles, lines, balls and half-planes under the Möbius transformations. [ABSTRACT FROM AUTHOR]

A version of the Arzelà-Ascoli theorem for X being a σ-locally compact Hausdorf space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and Urysohn operators, are derived on the basis of Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]