On local attractivity of    nonlinear functional integral equations via measures of noncompactness

B. C. Dhagea,* S. B. Dhagea, S. K. Ntouyasb,† and H. K. Pathakc,‡

On local attractivity of nonlinear functional integral equations via measures of noncompactness

Authors :

B. C. Dhage^a,*S. B. Dhage^a, S. K. Ntouyas^b,†and H. K. Pathak^c,‡

Author Address :

^aKasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India.
^bDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.
^cSchool of Studies in Mathematic, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India.

Abstract :

In this paper, we prove the local attractivity of solutions for a certain nonlinear Volterra type functional integral equations. We rely on a measure theoretic fixed point theorem of Dhage (2008) for nonlinear $mathcal{D}$-set-contraction in Banach spaces. Finally, we furnish an example to validate all the hypotheses of our main result and to ensure the existence and ultimate attractivity of solutions for a numerical nonlinear functional integral equation.

Keywords :

Measure of noncompactness, fixed point theorem, functional integral equation, attractivity of solutions.

DOI :

Article Info :

Received : December 11, 2014; Accepted : March 01, 2015.