A New Contraction and Associated φ-Fixed Point Results Using w-Distances with Applications to Third-order BVP and Integral Equations

In this paper we formulate and solve a problem in metric fixed point theory and show that the results obtained herein are actual generalizations of certain previous results. The problem is formulated by combining three different existing lines of research. We discuss illustrative examples and include two applications wherein an integral equation and a third-order boundary value problem are solved by application of our results obtained herein. The examples demonstrate the fact that the class of functions to which the previous results are applicable are augmented by the results of the present paper.