Nonlinear D-set contraction mappings in partially ordered normed linear spaces and applications to functional hybrid integral equations
Authors :
Bapurao C. Dhage
Author Address :
Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India.
Abstract :
n this paper the author introduces the notion of partially nonlinear D-set-contraction mappings in a partially ordered normed linear space and prove some hybrid fixed point theorems under certain mixed conditions from algebra, analysis and topology. The applications of abstract results presented here are given to perturbed nonlinear hybrid functional integral equations for proving the existence as well as global attractivity of the comparable solutions under certain monotonic conditions. The abstract theory developed in thispaper is also useful to develop the algorithms for the solutions of some nonlinear problems of analysis and allied areas of mathematics.
Keywords :
Partial measure of noncompactness; Partially nonlinear D-set-contraction mappings; Fixed points; Functional integral equation; Existence theorem; Attractivity of solutions
DOI :
Article Info :
Received : October 06, 2014; Accepted : November 04, 2014.
