Nonlinear $D$-set contraction mappings in partially ordered normed linear spaces and applications to functional hybrid integral equations

Bapurao C. Dhage

doi:10.26637/mjm301/007

Abstract

In 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 this paper 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, Fixed points, Functional integral equation, Existence theorem, Attractivity of solutions, Partially nonlinear $D$-set-contraction mappings

Mathematics Subject Classification:

45G10, 45M99, 47H09, 47H10

Authors Imprint References Funding Related Articles Downloads

Bapurao C. Dhage

Pages: 62-85
Date Published: 01-01-2015
Vol. 3 No. 01 (2015): Malaya Journal of Matematik (MJM)

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