An Introduction to Nonlinear Analysis and Fixed Point Theory by Hemant Kumar Pathak

Author:Hemant Kumar Pathak
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

(ii)There exists such that if R, and then

Then F has a nonzero fixed point with

The following result is the multivalued analogue of Krasnoselski’s fixed point theorem due to Agarwal and Regan [6] in a cone.

Let be a Banach space and . For let

Theorem 5.167

(Agarwal and Regan [6]) Let be a Banach space and a cone and let be increasing with respect to C. Also r, R are constants with . Suppose (here K(C) denotes the family of nonempty, convex, compact subset of C) is an upper semicontinuous, compact map and assumes one of the following conditions

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