Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

B. C. Dhage

Address. Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India

E-mail: bcd20012001@yahoo.co.in

Abstract. In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage [D4] under weaker convexity conditions.

AMSclassification. 47A25, 34A60.

Keywords. Ordered Banach space, hybrid fixed point theorem, neutral functional differential inclusion and existence theorem.