Some coincidence point results for T-contraction mappings on partially ordered b-metric spaces and applications to integral equations

In this paper, we prove some fixed point results for T-contraction mappings in partially ordered b-metric spaces, that generalize the main results of [H. Huang, S. Radenovič, J. Vujakovič, On some recent coincidence and immediate consequences in partially ordered b-metric spaces, Fixed Point Theory Appl., 2015, Paper No. 63]. As an application, we discuss the existence for a solution of a nonlinear integral equation

Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces

Coincidence point and common fixed point results with the concept of generalized altering distance functions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. As an application, we study the existence of a common solution to a system of integral equations

Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

In the present article, we introduce a unified notion of multi-tupled fixed points and utilize the same to prove some existence and uniqueness unified multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions satisfying generalized mixed monotone property in ordered metric spaces. Our results unify several classical and well-known n-tupled (including coupled, tripled and quadrupled ones) fixed point results existing in the literature.Comment: arXiv admin note: substantial text overlap with arXiv: 1601.0251

Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

[EN] We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.This second author acknowledges the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals for funding this work through the projects IN151014 and IN141047.Choban, MM.; Berinde, V. (2017). Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance. Applied General Topology. 18(2):317-330. https://doi.org/10.4995/agt.2017.7067SWORD31733018

Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space

In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation