This paper is twofold. First we prove a common fixed point theorem for a pair of weakly compatible mappings along with E.A. property. This theorem improves and generalizes a result of Jungck [5] without any continuity requirement besides relaxing the containment of the range of one map into the range of other map. Moreover, we prove some results under different variants of R-weakly commuting ma...

This paper presents a common fixed point theorem for a family of R-weakly commuting mappings satisfying nonlinear type contractive conditions. This result improves and unifies previous results due to O’Regan and Saadati [D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008) 86–93]. Also, the following results will be probabilistic version...

Some fixed and coincidence point theorems for R-weakly commuting mappings are obtained. Our results generalize some recent results of Daffer and Kaneko [2] and many of the others. AMS Mathematics Subject Classification (2000): 54H25

Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...

The aim of the present paper is to prove a common fixed point theorem for six mappings via pointwise R-weakly commuting mappings in probabilistic metric spaces satisfying contractive type implicit relations. This generalizes several known results in the literature including those of Kumar and Pant (Filomat 22:2 (2008), 43-52), Kumar and Chugh (Sci. Math. Japan. 56 (2002), 269-275) and others. M...

The aim of this paper is to obtain a common fixed point theorem in an intuitionistic fuzzy metric space for pointwise R-weakly commuting mappings using contractive condition of integral type and to establish a situation in which a collection of maps has a fixed point which is a point of discontinuity.

The purpose of this paper is to present a common fixed point theorem for pair R-weakly commuting mappings defined on b-fuzzy metric spaces satisfying nonlinear contractive conditions Boyd-Wong type, obtained in D. W. Boyd, J. S. Wong: On contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...

In this paper, first we prove fixed point theorems for different variant of compatible maps, satisfying a contractive condition of integral type in fuzzy metric spaces, which improve the results of Branciari [2], Rhoades [33], Kumar et al. [23], Subramanyam [35] and results of various authors cited in the literature of ”Fixed Point Theory and Applications”. Secondly, we introduce the notion of ...