A study of common fixed points that belong to zeros of a certain given function with applications

In this paper, we establish some point of φ-coincidence and common φ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations

Proving Fixed-Point Theorems Employing Fuzzy (σ, Z)-Contractive-Type Mappings

In this article, the concept of fuzzy (σ, Z)-contractive mappings is introduced in the setting of fuzzy metric spaces. Thereafter, we utilize our newly introduced concept to prove some existence and uniqueness theorems in M-complete fuzzy metric spaces. Our obtained theorems extend and generalize the corresponding results in the existing literature. Moreover, some examples are adopted to exhibit the utility of the newly obtained result

Fixed points which belong to the set of unit values of a suitable function on fuzzy metric spaces

[EN] In this paper, we introduce the notion of fuzzy (F,ϕ,β-ψ)-contractive mappings in fuzzy metric spaces and utilize the same to prove some existence and uniqueness fuzzy ϕ-fixed point results in both M-complete and G-complete fuzzy metric spaces. The obtained results extend, generalize and improve some relevant results of the existing literature. An illustrative example is utilized to demonstrate the usefulness and effectiveness of our results.This study was supported by Thammasat University Research Fund, Contract No TUFT 52/2565.Saleh, HN.; Imdad, M.; Sintunavarat, W. (2023). Fixed points which belong to the set of unit values of a suitable function on fuzzy metric spaces. Applied General Topology. 24(1):9-24. https://doi.org/10.4995/agt.2023.1692492424

New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces

In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results

Fixed Circle and Fixed Disc Results for New Types of Θc-Contractive Mappings in Metric Spaces

In this manuscript, we introduce the notions of various types of Θc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings, which generalize many results of invariance and transformations in the literature