Abstract
AbstractCoincidence and fixed point theorems for a new class of hybrid contractions consisting of a pair of single-valued and multivalued maps on an arbitrary nonempty set with values in a metric space are proved. In addition, the existence of a common solution for certain class of functional equations arising in dynamic programming, under much weaker conditions are discussed. The results obtained here in generalize many well known results.
Highlights
Nadler’s multivalued contraction theorem 1 see Covitz and Nadler, Jr. 2 was subsequently generalized among others by Reich 3 and Ciric 4
For a fundamental development of fixed point theory for multivalued maps, one may refer to Rus 5
Suzuki 9, Theorem 2 obtained a forceful generalization of the classical Banach contraction theorem in a remarkable way
Summary
Nadler’s multivalued contraction theorem 1 see Covitz and Nadler, Jr. 2 was subsequently generalized among others by Reich 3 and Ciric 4. For a fundamental development of fixed point theory for multivalued maps, one may refer to Rus 5. That is, contractive conditions involving single-valued and multivalued maps are the further addition to metric fixed point theory and its applications. Its further outcomes by Kikkawa and Suzuki 10, , Mot and Petrusel and Dhompongsa and Yingtaweesittikul , are important contributions to metric fixed point theory. In this paper we obtain a coincidence theorem Theorem 3.1 for a pair of single-valued and multivalued maps on an arbitrary. Fixed Point Theory and Applications nonempty set with values in a metric space and derive fixed point theorems which generalize Theorem 2.1 and certain results of Reich 3 , Zamfirescu 14 , Mot and Petrusel 12 , and others. We deduce the existence of a common solution for Suzuki-Zamfirescu type class of functional equations under much weaker contractive conditions than those in Bellman , Bellman and Lee , Bhakta and Mitra , Baskaran and Subrahmanyam , and Pathak et al
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