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In this paper, the notion of generalized set-valued weak - contractions is introduced and a new fixed point theorem for such contractions is established in the setting metric spaces. The main result is a generalization of fixed point theorems in the literature. An example and an application to generalized differential equation are given to support the validity of the main theorem.

abstract and applied analysis

Fixed Point Theorems for Generalized Set-Valued Weak <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>θ</mml:mi></mml:math>-Contractions in Complete Metric Spaces

Fixed Point Theorems for Generalized Set-Valued Weak θ-Contractions in Complete Metric Spaces