The classical theorems in projective geometry involve constructions based on points and straight lines. A general feature of these theorems is that a surprising coincidence awaits the reader who makes the construction. A classical example of this is Pappus’s theorem. One starts with 6 points, 3 of which are contained on one line and 3 of which are contained on another. Drawing the additional li...

In this paper we define a new weak contractive condition for a pair of self mappings in fuzzy metric space and prove the existence of coincidence and common fixed points. Mathematics Subject classification: 47H1, 54A40, 54E99

In this paper, we present some fixed and coincidence point theorems for hybrid rational Geraghty contractive mappings in partially ordered $b$-metric spaces. Also, we derive certain coincidence point results for such contractions. An illustrative example is provided here to highlight our findings.

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

Recently, Choudhury and Metiya [Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of the Banach's contraction mapping, which have been studied by several authors. In this paper, we introduce the notion of $f$-weak contractions and als...

March-April RANDOM COINCIDENCE POINTS FOR MULTI-VALUED NON-LINEAR CONTRACTIONS IN PARTIALLY ORDERED METRIC SPACES N. Shafqat , N. Yasmin , Z. Akhter c a,b Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800,Pakistan. c Department of Mathematics, The Islamia University Bhawalpur [email protected], [email protected], [email protected] A...

This is the continuation of the paper which appeared in the January, 1926, number of these Transactions.! Its chief object is to extend to an Mn with a boundary the results already obtained for transformations of manifolds without boundary. To these already treated in full we devote a few pages chiefly to elucidate and simplify certain points of importance for the extension. We have succeeded i...

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is essentially a generalization of Dekking coincidence t...

In this paper, tripled coincidence points of mappings satisfying some nonlinear contractive conditions in the framework of partially ordered Gb-metric spaces are obtained. Our results extend the results of Aydi et al. (Fixed Point Theory Appl., 2012:101, 2012, doi:10.1186/1687-1812-2012-101). Moreover, some examples of the main result are given. Finally, some tripled coincidence point results f...