Point Theorem In Quasi-metric Spaces Research Articles

"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects"

"A very impressive research work has been devoted in the last two decades to obtaining fixed point theorems in quasimetric spaces (also called b-metric spaces). Some incorrect and incomplete references with respect to the early developments on fixed point theory in b-metric spaces are though perpetually taking over from the existing publications to the new ones. Starting from this fact, our main aim in this note is threefold: (1) to briefly survey the early developments in the fixed point theory on quasimetric spaces (b-metric spaces); (2) to collect some relevant bibliography related to this topic; (3) to discuss some other aspects of current interest in the fixed point theory on quasimetric spaces (b-metric spaces)."

On Bishop-Phelps partial order, variation mappings and Caristi's fixed point theorem in quasi-metric spaces

On Bishop-Phelps partial order, variation mappings and Caristi's fixed point theorem in quasi-metric spaces

Coupled fixed point theorems in quasimetric spaces without mixed monotonicity

In this paper, using the concepts of f-closed set and inverse f-closed set, we will prove some fixed point theorems for graphic contractions in complete quasimetric space. Then, as applications, coupled fixed point theorems in quasimetric spaces without the mixed monotonicity property are obtained.

Fixed point theorems in quasi-metric spaces and the specialization partial order

Fixed point theorems in quasi-metric spaces and the specialization partial order

Fixed Point Theorems for Set-Valued Mappings under Contractive Condition in Quasi-Metric Spaces

Abstract In this paper, we introduce the concept of a generalized weak contraction for set-valued mappings defined on quasi-metric spaces. We show the existence of fixed points for generalized weakly contractive set-valued mappings. Indeed, we have a generalization of Nadler’s fixed point theorem and Banach’s fixed point theorem in quasi-metric spaces and, further, investigate the convergence of iterate scheme of the form xn+1 ∈ Fxn with error estimates.

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

Abstract In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Some Fixed Point Theorems in Quasi-Metric Spaces

Some Fixed Point Theorems in Quasi-Metric Spaces