The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.
Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of our results. An application to solution of linear equations is given which illustrates the proper application of the results in spaces over Banach algebra.MSC: Primary 47H10; secondary 54H25
A generalised common fixed point theorem of Presic type for two mappings f: X X and T: X k X in a cone metric space is proved. Our result generalises many wellknown results.
Eldred and Veeramani proved a theorem which ensures the existence of a best proximity point of cyclic contraction in metric space. In this paper we prove the existence of best proximity points of cyclic contractions and generalize proximal contractions of first and second kinds in the setting of complete b-metric space, thereby ascertaining an optimal approximate solution to the equation T x = x in a b-metric space.
Extending the Presic type operators to modular spaces, we introduce generalised Presic type
w
-contractive mappings and strongly
w
-contractive mappings in a modular metric space and establish fixed-point theorems for such contractions in modular spaces. Ulam–Hyers stability of the fixed-point equation involving Presic type operators is also discussed. Our results extend and generalise some known results in the literature. The results are supported by appropriate example and an application to Caratheodory type integral equation.
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