In this paper, we extend and improve the condition of contraction of results of azam et al. The purpose of this paper is to prove common fixed point theorems for two banach pairs of mappings satisfying contractive condition including product in complex valued metric space using f. The obtained results are generalizations of recent results proved by dubey et al. Common fixed point, complex valued metric space, weakly compatible mappings.
Banach contraction principle in was the starting point for many researchers during last decades in the field of nonlinear analysis. Common fixed point theorems for weakly compatible mappings in complex valued metric space muhammad sarwar, mian bahadur zada, and saurabh manro abstract. In this paper, we prove certain common fixedpoint theorems for two singlevalued mappings in such spaces. The concept of complex valued bmetric spaces was introduced in 20 by rao et al.
Research article some common fixed point theorems in complex valuedmetric spaces aimana. Research article some common fixed point theorems in. Some common fixed point theorems on complex valued metric spaces. Common fixed point theorems in complex valued metric spaces. In this paper, we prove common fixed point theorems under patas condition in complex valued metric spaces and we apply our main theorem to establish the existence and the uniqueness of a common solution of a system of urysohn integral equations. Moreover, we improve several assumptions on the involved mappings. Applications and theorem on common fixed point in complex valued. The purpose of this article is to establish a new xed point theorem in the context of complex valued bmetric spaces and to generalize some results of complex valued metric spaces. Common fixed point theorems for multivalued mappings. Common fixed point theorems in complex valued metric spaces article in numerical functional analysis and optimization 323. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixedpoint theorems due to rouzkard and imdad 2012. Kumam, generalized common fixed point theorems in complex valued metric spaces and applications, journal of inequalities and applications, vol. 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 pointdependent control functions as coefficients in complex valued metric spaces. Fixedpoint theory in complex valued metric spaces has greatly developed in recent times.
Generalized common fixed point theorems in complex valued. Pdf generalized common fixed point theorems in complex. Department of mathematics, kalna college, kalna, burdwan, west bengal, india. In this paper, first we prove a common fixed point theorem for a p air of weakly compatible self maps in complex valued metric space for rational inequality. In this article, we utilize the notions of the property e.
Some common fixed point theorems in complex valued metric spaces article pdf available in the scientific world journal 20141 may 2014 with 146 reads how we measure reads. Common fixed point theorems in digital metric spaces. The self maps and of a non newtonian metric space, are said to be weakly commutative iff. Recently, the concept of complex valued metric spaces was introduced by azam et al. Common fixed point theorems satisfying contractive type. Pdf the aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general. Common fixed point theorems in complex valued metric. In this paper, we continue the study of fixed point theorems in complex valued metric spaces. Generalized common fixed point theorems in complex valued metric spaces and applications.
Some common fixed point results in complex valued metric. In the same way, sintunavarat and kumam 19, 20 obtained common fixed point results by replacing the constant of contractive condition to control functions. Our results unify, generalize and complement the comparable. Generalized common fixed point theorems in complex valued metric spaces and applications article pdf available in journal of inequalities and applications 20121. Common fixed point theorems in complex valued metric spaces manoj kumar1. Common fixed points for multivalued mappings in complex valued metric spaces with applications ahmad, jamshaid, klineam, chakkrid, and azam, akbar, abstract and applied analysis, 20. In this article, we extend and improve the condition of contraction of the results of azam et al. Pathak, common fixed point theorems using property e. There exist various paper on complex valued metric spaces such as 1, 3, 9, 12, 18 and, 14.
In this paper, we generalized the result some common fixed point theorems in complex valued metric spaces of mala hakwadiya, r k gujetiya, dheeraj kumara mali 6. Journal of inequalities and applications common fixed point theorems for multivalued mappings in complexvalued metric spaces akbar azam 0 jamshaid ahmad 0 poom kumam 1 0 department of mathematics, comsats institute of information technology, chack shahzad, islamabad, 44000, pakistan 1 department of mathematics, faculty of science, king mongkuts university of technology. In this paper we obtain a common fixed point theorem for six maps in complex valued metric spaces having commuting and weakly compatible and satisfying different type of inequality. The obtained results are generalizations of recent results proved by dubey et. Common fixed point theorems for contractive type mappings.
The obtained results are generalizations of recent results proved by sintunavarat and kumam, rouzkard and imdad. Then s and t have a unique common fixed point in this paper, we continue the study of fixed point theorems in complex valued metric spaces. A along with weak compatibility of pairs are proved and further some results using clrproperty are obtained in complex valued metric spaces which generalize various results of ordinary metric spaces. Based on the discussion above, for our purpose, we first prove the existence of common fixed point theorems for multivalued mapping in. In 2 the authors introduced the notion of complexvalued metric space and obtained a common fixed point theorems of contraction type. In this paper, first we prove a common fixed point theorem for a pair of weakly compatible self maps in complex valued metric space for rational inequality. Research article common fixed point theorems satisfying. Issn online 23473207 common fixed point theorems in. A common fixed point theorem in metric spaces springerlink. Though complex valued metric spaces form a special class of cone metric space, yet this idea is intended to define rational expressions which are not meaningful. Research open access generalized common fixed point. In this paper, common fixed point theorems for a pair of mappings satisfying certain rational contractions are established in the framework of complex valued b metric spaces. Complex valued metric spaces and common fixed point. Common fixed point theorems for contractive type mappings in complex valued metric spaces.
Pdf common fixed point theorems in complex valued metric. We get some improved versions of several fixed point theorems in complete metric spaces. We prove a common fixed point theorem for a pair of mappings. A note on fixed point results in complexvalued metric spaces. In sequel, mukheimer proved some common fixed point theorems in complex valued metric spaces. In this paper we prove a common fixed point theorem for two selfmappings in complex valued bmetric spaces under contractive condition. We introduce complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying contractive. Fixed point theorems in complex valued metric spaces sciencedirect. Mukheimer department of mathematical sciences, prince sultan university, riyadh, saudi arabia.
Let x, d be a complete complex valued metric space and s, t. Some fixed point theorems in complex valued metric spaces. In 1989, bakhtin introduced the concept of bmetric space as a generalization of metric spaces. Common fixed point theorem in complex valued metric spaces. In 32, saluja proved some fixed point theorems under rational contraction in the setting of complex valued metric spaces. A common fixed point result in complex valued bmetric spaces under contractive condition. Common fixed point theorems for a rational inequality in. Common fixed point theorems in complex valued metric space.
Some common fixed point theorems in complex valued b. Coupled coincidence point theorems for new types of mixed monotone multivalued mappings in partially ordered metric spaces klanarong, chalongchai and suantai, suthep, abstract and applied. Some common fixed point theorems on complex valued metric. Common fixed point theorems in modified intuitionistic. Common and coincidence fixed point theorems under rational. Fixed point theorems in complex valued metric spaces. Some common fixed point theorems in complex valued metric. Common fixed point theorems for multivalued mappings in. Common fixed point theorems of single and setvalued.
Weakly compatible maps, fixed points, common fixed points, complex valued metric spaces. Some common fixed point theorems in complex valued metric spaces. Some common fixed point theorems satisfying certain rational expressions are proved in complex valued metric spaces which generalize fixed point theorems due to azam et al. These results are the generalization of varioustheorems of ordinary and fuzzy metric spaces. Some related results are also derived besides furnishing illustrative examples to. Also, we prove a common fixed point theorem for pairs of selfmappings along with weakly commuting property. Complex valued metric space, closed ball, common fixed point 1. Kumam, generalized common fixed point in complex valued metric spaces and applications. Common fixed points of fcontraction mappings in complex. A common fixed point result in complex valued bmetric. A properties of the involved pairs, common xed point results for four and six weakly compatible selfmappings are established in complex valued metric. Some new common fixed point theorems in complex valued bmetric spaces durdana lateef abstract. In this paper, the existence of common fixed points is established for multi valued mappings on the complexvalued metric spaces.
Common fixed point theorems under patas contraction in. Secondly, we prove common fixed point theorems for weakly compatible mappings along with. In sequel, mukheimer proved some common xed point theorems in complex valued metric spaces. Our theorem generalizes and extends the results of said researcher. Common fixed point theorems under rational contractions in complex valued metric spaces.
Pdf some common fixed point theorems in complex valued. Khan, common fixed point theorems in complex valued metric spaces, numerical functional analysis and optimization, vol. Request pdf common fixed point theorems in complex valued metric spaces we introduce complex valued metric spaces and obtain sufficient conditions. Pdf fixed point theorems in complex valued metric spaces. Complex valued metric space is useful in many branches of mathematics. In this paper, the existence of common fixed points is established for multivalued mappings on the complexvalued metric spaces. In this article, we modified and generalized a contraction mapping of azam et al. Some common fixed point theorems satisfying contractive conditions involving rational expressions and product for four mappings that satisfy property e.
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