Abstract
A new proper generalization of metric called as θ -metric is introduced by Khojasteh et al. (Mathematical Problems in Engineering (2013) Article ID 504609). In this paper, first we prove the Caristi type fixed point theorem in an alternative and comparatively new way in the context of θ -metric. We also investigate two θ -metrics on CB ( X ) (family of nonempty closed and bounded subsets of a set X). Furthermore, using the obtained θ -metrics on CB ( X ) , we prove two new fixed point results for multi-functions which generalize the results of Nadler and Lim type in the context of such spaces. In order to illustrate the usability of our results, we equipped them with competent examples.
Highlights
A wide range of pertinence made fixed point theory one of the most attractive areas of research in nonlinear analysis and mathematics
In an effort to generalize Banach ContractionPrinciple (BCP), which holds in all complete metric spaces, to a wide class of spaces, Khojasteh et al [16] coined the notion of θ-metric
The results presented here generalize various results of the metric fixed point theory
Summary
A wide range of pertinence made fixed point theory one of the most attractive areas of research in nonlinear analysis and mathematics. An interesting and fruitful generalization of the Banach Contraction Principle (BCP) on a complete metric space is the Caristi fixed point theorem (Caristi’s FPT) [10]. In an effort to generalize BCP, which holds in all complete metric spaces, to a wide class of spaces, Khojasteh et al [16] coined the notion of θ-metric. They characterized the BCP and Caristi type fixed point theorems in the setting of θ-metric space. Fixed point theorems for multifunction in the context of θ-metric spaces are proved, which generalize various metric fixed point results.
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