Jñānābha‎, Vol. 49 (1) (2019), 50-66

EXISTENCE THEOREMS FOR A PBVP OF FIRST ORDER FUNCTIONAL RANDOM INTEGRODIFFERENTIAL INCLUSIONS

Bapurao C. Dhage

"Kasubai", Gurukul Colony, Thodga Road
Ahmedpur - 413515, Dist. Latur, Maharashtra, India
Email:bcdhage@gmail.com
(Received : May 11, 2019 ; Revised: May 24, 2019)



Abstract

In this paper, some existence theorems for a periodic boundary value problem of first order ordinary functional random integrodifferential inclusions are proved for convex and nonconvex cases of random multi-valued functions involved in the inclusion. The existence theorems for external random solutions are also proved under certain monotonic conditions of the multi-valued function. The multi-valued random .fixed point theoretic approach of Dhage (2011) is used while establishing the results concerning the existence of external random solutions.


2010 Mathematics Subject Classifications47H07, 47H10, 60H25.
Keywords and phrasesRandom integro-differential inclusion; Random fixed point theorem; Existence theorem.