In this paper, a concept of monotone generalized contraction in partially ordered metric spaces is introduced and some fixed point and common fixed point theorems for the so-called weak contractions are proved. The concept of weak contraction was introduced by Kada, Suzuki and Takahashi [Math. Japonica, 44 (1996), 381-391], in connection to the concept of w-distance on a metric space. The resul...

In this paper, we introduce a new concept on a complete generalized D∗-metric space by using the concept of generalized D∗-metric space (D∗-cone metric space) called ∇∗∗-distance and, by using the concept of the ∇∗∗-distance we prove some new fixed point theorems in complete partially ordered generalized D∗-metric space which is the main result of our paper. c ©2015 All rights reserved.

‎The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎Also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎The results presented in the paper generalize and extend several well-known results in the literature‎.

In this note we point out and rectify some errors in a recently published paper “N. Singh, R. Jain: Coupled Fixed Point Results For Weakly Related Mappings In Partially Ordered Metric Spaces, Bull. Iranian Math. Soc. 40 (2014), no. 1, 29-40”.

* Correspondence: radens@beotel. net Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Beograd 11120, Serbia Full list of author information is available at the end of the article Abstract We introduce ordered quasicontractions and g-quasicontractions in partially ordered metric spaces and prove the respective coincidence point and (common) fixed point results. An e...

In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example.