Fixed point theorems for generalized contraction mappings in multiplicative metric spaces

Abstract

The purpose of this paper is to study and discuss the existence of common fixed points for weakly compatible mappings satisfying the generalized contractiveness and the (CLR)-property. Our results improve the corresponding results given in He et al. [X. He, M. Song, D. Chen, Fixed Point Theory Appl., 2014, 9 pages]. Moreover, we give some examples to illustrate for the main results.

Metrical Fixed Point Results on \lowercase{b}-multiplicative metric spaces employing binary relaion

“…The main idea behind introducing MMS was to replace usual triangular inequality by the multiplicative triangle inequality. Later on, many research papers were written on fixed points in MMS [11][12][13][14][15][16][18][19][20]. Czerwik [17] introduced the notion of b-metric space which is a generalization of metric space.…”

Some Fixed Point Results on Multiplicative Metric Spaces

“….Dosenaovic and Radenovic [5] prove the existence of fixed point of contractions rational type in multiplicative metric spaces. Also, Abdou [6] prove fixed point theorems for generalized contraction mappings in multiplicative metric spaces. Other result about fixed point theory in multiplicative metric space can be seen in [7], [8], [9], [10], and [11] In this article, we prove some fixed points results in multiplicative metric space.…”

Some fixed points of multivalued maps in multiplicative metric spaces

“…Some of the properties satisfied by the multiplicative distance gave birth to the general concept of multiplicative metrics, defined as alternative to standard metrics. It was noted in [1] that the set of positive real numbers is not complete in the usual topology (induced by the standard metric ) but it is complete for the multiplicative metric . On the other hand, a sequence of positive real numbers is convergent with respect to d if and only if it is convergent with respect to .…”