• D. M. Suryawanshi
• S.S. Bellale

In this paper we have proved the existence of the solution of perturbed abstract measure differential equation by using Dhage’s iteration method. The main result is based on the iteration method included in the hybrid fixed point theorem in a partially ordered normed linear space. Also we have solved an example for the applicability of given results in the paper. Sharma [23] initiated the study of nonlinear abstract differential equations and some basic results concerning the existence of solutions for such equations. Later , such equations were studied by various authors for different aspects of the solutions under continuous and discontinuous nonlinearities. The study of fixed point theorem for contraction mappings in partial ordered metric space is initiated by different authors. The study of hybrid fixed point theorem in partially ordered metric space is initiated by Dhage[3,4,5] with applications to nonlinear differential and integral equations. The iteration method is also embodied in hybrid fixed point theorem in partially ordered spaces by Dhage[19,20]. In this paper we adopted this iteration method technique for abstract measure differential equations.

Abstract measure differential equation, Dhage iteration method, existence theorem, extremal solutions ,approximation of solution, hybrid fixed point theorem.

"ITERATION METHOD FOR APPROXIMATING SOLUTIONS OF PERTURBED ABSTRACT MEASURE DIFFERENTIAL EQUATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 4, page no.746-752, April-2019, Available :http://www.jetir.org/papers/JETIR1904R14.pdf

"ITERATION METHOD FOR APPROXIMATING SOLUTIONS OF PERTURBED ABSTRACT MEASURE DIFFERENTIAL EQUATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 4, page no. pp746-752, April-2019, Available at : http://www.jetir.org/papers/JETIR1904R14.pdf