Abstract
AbstractCoincidence and fixed point theorems for a new class of contractive, nonexpansive and hybrid contractions are proved. Applications regarding the existence of common solutions of certain functional equations are also discussed.
Highlights
The following remarkable generalization of the classical Banach contraction theorem, due to Suzuki 1, has led to some important contribution in metric fixed point theory see, e.g., 1–8 .Theorem 1.1
As a generalization of the results of Goebel 13, Edelstein 22 and Naimpally et al 14, Corollary 3, we extend Theorem 2.1 for a pair of Suzuki contractive maps S, T : Y → X cf. 2.2 and 2.3, wherein X, d is a metric space
We present the following extension of Theorem 3.1 for a pair of Suzuki nonexpansive maps cf. 3.2
Summary
The following remarkable generalization of the classical Banach contraction theorem, due to Suzuki 1 , has led to some important contribution in metric fixed point theory see, e.g., 1–8. Fixed point theorems for nonexpansive maps due to Browder 10, and Gohde have been generalized in 6 cf Theorem 3.1 below. Combining the ideas of Suzuki 6, 7 , Goebel and Naimpally et al , first we generalize Theorems 2.1 and 3.1 to a wider class of maps on an arbitrary nonempty set with values in a metric resp. Using the notion of IT-commuting maps due to Itoh and Takahashi , we obtain generalizations of multivalued fixed point theorems due to Reich , Iseki , Kikkawa and Suzuki 2 , Mot and Petrusel 3 , Dhompongsa and Yingtaweesittikul 4 and others to the case of Suzuki generalized hybrid contraction cf Theorem 4.1. We deduce the existence of a common solution for the Suzuki class of functional equations under much weaker conditions than those in 19–21
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