Jñānābha‎, Vol. 49 (2) (2019), 82-93

ON EXISTENCE AND UNIQUENESS THEOREMS FOR ABSTRACT MEASURE INTEGRODIFFERENTIAL EQUATIONS

By

Bapurao C. Dhage1 and P. Ram Mohan Reddy2

1"Kasubai", Gurukul Colony, Thodga Road, Ahmedpur - 413515, Dist. Latur, Maharashtra, India

Email:bcdhage@gmail.com

2Department of Mathematics, Government Degree College, Dharpally-503 165, Distr. Nizamabad, Telengana State, India

Email:rammohan09reddy@gmail.com

(Received : November 02, 2019 ; Revised: November 11, 2019)


Abstract

In this paper, we prove the relevance, existence and uniqueness theorems for a nonlinear abstract measure integrodifferential equation via classical .fixed point theorems of Schauder [14] and Dhage [10] under weaker Carathéodory condition. Our hypotheses and claims have also been illustrated with a couple of examples.


2010 Mathematics Subject Classification34K10, 47H10
Keywords and phrasesAbstract measure integrodifferential equation; Existence and uniqueness theorem