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In this paper, the author presents some generalizations of a measure theoretic hybrid fixed point theorem of Dhage for the monotone nondecreasing mappings in a partially ordered metric space and then applies to a nonlinear functional integral equation for proving the existence as well as local ultimate attractivity of the comparable solutions defined on a unbounded interval of real line. An algorithm is constructed and it is shown that the sequence of successive approximations of the considered integral equation converges monotonically to the solution under weak partial Lipschitz and partial compactness type conditions.

Some generalizations of a hybrid fixed point theorem in partially ordered metric spaces and nonlinear functional integral equations