Fixed and common fixed point theorems in frame of quasi metric spaces under contraction condition based on ultra distance functions

In this paper, we introduce the notion of ultra distance function. Based on the notion of ultra distance function, we introduce the definitions of (k, ψ, L)-quasi contractions of type (I) and type (II) in the frame of quasi metric spaces. We employ our new definitions to construct and prove many fixed and common fixed point results in the frame of quasi metric spaces. Our results extend and improve many exciting results in the literatures. Also, we introduce some examples and some applications in order to support the usability of our work

Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces

AbstractThe purpose of this paper is to establish a coupled coincidence point for a pair of commuting mappings in partially ordered complete metric spaces. We also present a result on the existence and uniqueness of coupled common fixed points. An example is given to support the usability of our results

New theorems on extended b-metric spaces under new contractions

The notion of extended b-metric space plays an important role in the field of applied analysis to construct new theorems in the field of fixed point theory. In this paper, we construct and prove new theorems in the filed of fixed point theorems under some new contractions. Our results extend and modify many existing results in the literature. Also, we provide an example to show the validity of our results. Moreover, we apply our result to solve the existence and uniqueness of such equations

Solvability of a system of integral equations in two variables in the weighted Sobolev space W(1,1)-omega(a,b) using a generalized measure of noncompactness

In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b). The results were achieved by equipping the space E with the vector-valued norms and using the measure of noncompactness constructed in [F.P. Najafabad, J.J. Nieto, H.A. Kayvanloo, Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations, J. Fixed Point Theory Appl., 22(3), 75, 2020] to applicate the generalized Darbo’s fixed point theorem [J.R. Graef, J. Henderson, and A. Ouahab, Topological Methods for Differential Equations and Inclusions, CRC Press, Boca Raton, FL, 2018]

Existence of Fixed Point Results in -Metric Spaces

The purpose of this paper is to prove the existence of fixed points of contractive mapping defined on -metric space where the completeness is replaced with weaker conditions. Moreover, we showed that these conditions do not guarantee the completeness of -metric spaces

Tripled and coincidence fixed point theorems for contractive mappings satisfying Φ-maps in partially ordered metric spaces

Abstract In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X × X × X → X and g : X → X satisfying a nonlinear contraction based on φ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results

Some cyclic fixed point results for contractive mappings

In this paper, we obtained some new cyclic type generalize, improve and enrich some recent results fixed point theorems using C-class functions in the in the existing literature. framework of metric spaces. Our results extend, generalize, improve and enrich some recent results in the existing literature