Fixed point theorems for ( α , φ )-contractive mappings of rational type in complex valued metric spaces with applications (original) (raw)
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Results in Fixed Point Theory and Applications
A very interesting approach in the theory of contractive mappings was recently given by Samet et al. (Nonlinear Anal. 75, 2012, 2154-2165) by using the concept of α-ψ contractive type mappings in metric spaces. The purpose of this paper is to give the generalized version of α-ψ contractive type mappings in complex valued metric spaces. For this, we define the notion of (α, φ)-contractive mappings of rational type and obtain fixed point theorems for such mappings in the framework of complex valued metric spaces. This extends and subsumes the recent results of Azam et al.
Common fixed point theorem for Chatterjea-Type Contractive mapping in Complex Valued Metric Space
Study of Multivalued contraction mapping was initiated by Nadler[1] and Markin[2]. There are so many research papers in which multiple common fixed point theorem results are proved by authors[3-10].This paper deals with some common fixed point theorems which are established for multi valued mapping in complex valued metric space as Azam et al.(numer.Funct.anal.Optim.33(5):590-600,2012) introduced the notion of complex valued metric space and proved some common fixed point theorems in the context of complex valued metric space. Keywords: multi-valued mapping, common fixed point, complex valued metric space.
Fixed point theorems in complex valued metric spaces
Journal of the Egyptian Mathematical Society, 2016
The aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex valued metric spaces. Our results generalize and extend the results of Azam et al. (2011) [1], Sintunavarat and Kumam (2012) [2], Rouzkard and Imdad (2012) [3], Sitthikul and Saejung (2012) [4] and Dass and Gupta (1975) [5]. To substantiate the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also furnished.
Fixed Point Theorem for Mappings in Complex Valued Metric Space
In [1] Azam et al introduced the notion of complex valued metric spaces and obtained common fixed-point result for mappings in the context of complex valued metric spaces. In this paper, existence of common fixed point is established for two mappings satisfying certain rational inequality on complex valued metric space followed by the consequences of the main result. These results complement the comparable results from the current literature.
Common Fixed Point Theorem for Contractive Mappings in Complex Valued -Metric Spaces
gazi university journal of science, 2016
In this paper, we present some common fixed point results for the contractive mappings on complex valued bbb-metric spaces and obtain a generalization of theorem of Azam et al., \cite{Az}, Klin-eam and Suanoom \cite{Kl}, Mukheimer \cite{Mu}, Rouzkard and Imdad \cite{Ro}, Sitthikul and Saejung \cite{Si} and Sintunavarat and Kumam \cite{Sk}.