We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

We consider a generalized Pompeiu equation in the space of Schwartz distributions and as an application we find the locally integrable solutions of the equation. © 2005 Elsevier Ltd. All rights reserved. MSC: 39B22; 47H15; 46F05

We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers ...

in this paper, we prove the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to conrm our theorem.