Abstract
Using the generalized Caristi's fixed point theorems we prove the existence of fixed points for self and nonself multivalued weaklyw-contractive maps. Consequently, Our results either improve or generalize the corresponding fixed point results due to Latif (2007), Bae (2003), Suzuki, and Takahashi (1996) and others.
Highlights
It is well known that Caristi’s fixed point theorem 1 is equivalent to Ekland variational principle 2, which is nowadays is an important tool in nonlinear analysis
Using the concept of Hausdorff metric, Nadler Jr. 7 has proved multivalued version of the Banach contraction principle which states that each closed bounded valued contraction map on a complete metric space, has a fixed point
Bae 4 introduced a notion of multivalued weakly contractive maps and applying generalized Caristi’s fixed point theorems he proved several fixed point results for such maps in the setting of metric and Banach spaces
Summary
It is well known that Caristi’s fixed point theorem 1 is equivalent to Ekland variational principle 2 , which is nowadays is an important tool in nonlinear analysis. Bae 4 introduced a notion of multivalued weakly contractive maps and applying generalized Caristi’s fixed point theorems he proved several fixed point results for such maps in the setting of metric and Banach spaces. Using the concept of w-distance 8 , Suzuki and Takahashi 9 introduced a notion of multivalued weakly contractive in short, w-contractive maps and improved the Nadler’s fixed point result without using the concept of Hausdorff metric.
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