Search

In 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.

The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular metric spaces. As applications of our theorems, we deduce certain well-known results in b-metric spaces as corollaries.

We determine the multipliers M (X , Y) where X, Y ∈ { w 0 , w , w ∞ } , and we apply these results to the solvability of both the (SSIE) of the form F ⊂ E + w x , where F ∈ { w 0 , w , w ∞ } , and the (SSIE) w ⊂ E + W x 0 and w ⊂ E + W x . [ABSTRACT FROM AUTHOR]

In this article, we study the existence of a common best proximity points for a finite class of cyclic relatively nonexpansive mappings in the setting of Busemann convex spaces. In this way, we extend the main results given in Eldred and Raj (2009) [A.A. Eldred, V.S. Raj, On common best proximity pair theorems, Acta Sci. Math. (Szeged), 75, 707-721] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. We then present a strong convergence theorem of a common best proximity point for a pair of cyclic mappings in uniformly convex Banach spaces by using the Ishikawa iterative process. [ABSTRACT FROM AUTHOR]

In this sequel, we introduce and study the concept of the weak orthogonal metric spaces as a generalization of the orthogonal metric spaces. Besides, we define and study the generalized quasi-contractions on such spaces and illustrate several non-trivial examples to endorse our obtained results. Among other things, as corollaries we obtain the main results of some of the pioneering articles existing in the literature. Finally, we answer the open question posed by Gordji et al. [On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2):569-578, 2017]. [ABSTRACT FROM AUTHOR]

A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness of the space is equivalent to fixed point property for a larger class of mappings that includes continuous as well as discontinuous mappings. In addition to it, a probabilistic fixed point theorem satisfying (o-d) type non-expansive mappings is established. [ABSTRACT FROM AUTHOR]

We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued) cone metric spaces. Examples are given to distinguish our results from the known ones.

We consider quasicontraction nonself-mappings on Takahashi convex metric spaces and common fixed point theorems for a pair of maps. Results generalizing and unifying fixed point theorems of Ivanov, Jungck, Das and Naik, and Ćirić are established.

T. Zamfirescu, [Fixed point theorems in metric spaces, Arch. Math. (Basel), 23 (1972), 292-298] obtained a very interesting fixed point theorem on complete metric spaces, by combining results of Banach, Kannan and Chatterjea. In this paper, we introduce the concept of Zamfirescu- Perov type cyclic contraction and obtain best proximity point theorems for such mapping in the frame work of regular cone metric spaces. Examples are given to support our results. Our results extend and generalize several comparable existing results in literature. [ABSTRACT FROM AUTHOR]