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In the paper, we consider some fixed point results of F -contractions for triangular α -admissible and triangular weak α -admissible mappings in metric-like spaces. The results on F -contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property ( F 1 ) of the strictly increasing mapping F : 0 , + ∞ → − ∞ , + ∞ . Our approach gives a proper generalization of several results given in current literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of coincidence best proximity point for multivalued Suzuki-type α -admissible mapping using θ -contraction in b-metric space. Some examples are presented here to understand the use of the main results and to support the results proved herein. The obtained results extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We improve and generalize some new results in fixed point theory in the context of partial b-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove a unique common coupled fixed point theorem for two pairs of w-compatible mappings in S b -metric spaces. We also furnish an example to support our main result. [ABSTRACT FROM AUTHOR]