On Solution of Boundary Value Problems via Weak Contractions

The aim is to present a new relational variant of fixed point result that generalizes various fixed point results of the existing theme for contractive type mappings. As an application, we solve a periodic boundary value problem and validate all assertions with the help of nontrivial examples. We also highlight the close connections of the fixed point results equipped with a binary relation to that of graph related metrical fixed point results. Radically, these investigations unify the theory of metrical fixed points for contractive type mappings.

Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings

We present new fixed points algorithms called multistep H-iterative scheme and multistep SH-iterative scheme. Under certain contractive-type condition, convergence and stability results were established without any imposition of the ’sum conditions’, which to a large extent make some existing iterative schemes so far studied by other authors in this direction practically inefficient. Our results complement and improve some recent results in literature.

Nonunique Fixed Point Results via Kannan F -Contraction on Quasi-Partial b -Metric Space

This paper is aimed at acquainting with a new Kannan F -expanding type mapping by the approach of Wardowski in the complete metric space. We establish some fixed point results for Kannan F -expanding type mapping and F -contractive type mappings which satisfy F -contraction conditions. Additionally, some new results are given which generalize several results present in the literature. Moreover, some applications and examples are provided to show the practicality of our results.

Common Fixed Point Theorems for Six Self Maps in FM-Spaces Using Common Limit in Range Concerning Two Pairs of Products of Two Different Self-maps

In this article, we do a study of common fixed point theorems for six self-maps in FM-Spaces using common limit in range property concerning two pairs of products of two different self-maps. We use the properties (CLRTH) and (CLRSR) along with contractive type implicit relations to prove our results. In support of our result, an example has been provided. Our findings are like those of Kumar and Chouhan [12]. Kumar and Chauhan demonstrated their primary result in [12] by improving and generalizing Aalam, Kumar, and Pants' [1] results. In past, many authors have done study of common fixed point using (E-A) property (like Aalam et. al. [1] proved results using this property), and then these results were improved and generalized by using common (E-A) property as this property is superior to (E-A) property, as the closeness of subspace is required to prove a required result on common fixed point by using these properties, which is a drawback. We improve and generalize all results on these properties using common limit in range property. The goal of this note is to refine and generalize Kumar and Chauhan's [12] results on a common fixed point, as well as some earlier comparable results.

Unique Fixed-Point Results in Fuzzy Metric Spaces with an Application to Fredholm Integral Equations

This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.

Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

Convex Structure in Generalized Fuzzy Metric Spaces

In this paper, we introduce the concept of convex structure in generalized fuzzy metric spaces and proved common fixed point theorems for a pair of self-mappings under sufficient contractive type conditions.

An Approach of Lebesgue Integral in Fuzzy Cone Metric Spaces via Unique Coupled Fixed Point Theorems

In the theory of fuzzy fixed point, many authors have been proved different contractive type fixed point results with different types of applications. In this paper, we establish some new fuzzy cone contractive type unique coupled fixed point theorems (FP-theorems) in fuzzy cone metric spaces (FCM-spaces) by using “the triangular property of fuzzy cone metric” and present illustrative examples to support our main work. In addition, we present a Lebesgue integral type mapping application to get the existence result of a unique coupled FP in FCM-spaces to validate our work.

Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

In this paper, we introduce the new concept of coupled fixed-point (FP) results depending on another function in fuzzy cone metric spaces (FCM-spaces) and prove some unique coupled FP theorems under the modified contractive type conditions by using “the triangular property of fuzzy cone metric.” Another function is self-mapping continuous, one-one, and subsequently convergent in FCM-spaces. In support of our results, we present illustrative examples. Moreover, as an application, we ensure the existence of a common solution of the two Volterra integral equations to uplift our work.