Coupled fixed points in complex partial metric spaces

Metric-like spaces, partial metric spaces and fixed points

By a metric-like space, as a generalization of a partial metric space, we mean a pair (X ,σ ), where X is a nonempty set and σ : X × X →R satisfies all of the conditions of a metric except that σ (x, x) may be positive for x ∈ X . In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our resul...

Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces

In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illus...

Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces

and Applied Analysis 3 Definition 2.3. Let X, p be a partial metric space. Then, 1 a sequence {xn} in X, p is called a Cauchy sequence if limn,m→∞p xn, xm exists and is finite ; 2 the space X, p is said to be complete if every Cauchy sequence {xn} inX converges, with respect to τp, to a point x ∈ X such that p x, x limn,m→∞ p xn, xm . Lemma 2.4. Let X, p be a partial metric space. a {xn} is a C...

Coupled Fixed Point Results in Complete Partial Metric Spaces

Coupled fixed and coincidence points for monotone operators in partial metric spaces

*Correspondence: [email protected] Department of Mathematics, King Abdulaziz University, P.O. Box: 80203, Jeddah, 21589, Saudi Arabia Abstract In this paper, we prove some coupled fixed point results for (φ ,φ)-weakly contractive mappings in ordered partial metric spaces. As an application, we establish coupled coincidence results without any type of commutativity of the concerned maps. Cons...