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This article is a revision and correction of the chapter book [S. Hadi Bonab, V. Parvaneh, Z. Bagheri, ηA-Admissible Mappings for Four Maps in C*-Algebra-Valued MP-Metric Spaces with an Application, In: P. Debnath, Delfim F. M. Torres, Yeol Je Cho, Advanced Mathematical Analysis and its Applications, CRC Press, 2023, 97-113.]. In this article, we first introduce the concept of η-admissible mapping in C* -algebra valued MP-metric spaces, which is a generalization and combination of ”modular metric spaces”, ”parametric metric spaces” and ”C* -algebra-valued metric spaces”. Then, for four mappings in these spaces, we prove several fixed-point theorems. We give an example and an application regarding the solvability of operator equations and integral equations, respectively, to support the new findings. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to introduce the notion of ℜ-extended b-metric spaces and prove some fixed point results in this space. An extensive set of nontrivial examples is given to justify the claims. [ABSTRACT FROM AUTHOR]

In this study, we consider a nonlinear matrix equation of the form X = Q + ∑ i = 1 m A i ∗ G (X) A i , where Q is a Hermitian positive definite matrix, A i ∗ stands for the conjugate transpose of an n × n matrix A i , and G is an order-preserving continuous mapping from the set of all Hermitian matrices to the set of all positive definite matrices such that G (O) = O . We discuss sufficient conditions that ensure the existence of a unique positive definite solution of the given matrix equation. For this, we derive some fixed point results for Suzuki-FG contractive mappings on metric spaces (not necessarily complete) endowed with arbitrary binary relation (not necessarily a partial order). We provide adequate examples to validate the fixed-point results and the importance of related work, and the convergence analysis of nonlinear matrix equations through an illustration with graphical representations. [ABSTRACT FROM AUTHOR]

In this article, we introduce the concept of tripled controlled V -metric spaces and study Kannan type contractions in this new structure. Also, we extend the concept of Kannan type contractions to Kannan-Presic type contractions. Our results modify some known ones in the literature. To support our main results, an example and an application in integral equations are presented. [ABSTRACT FROM AUTHOR]

This article presents the E -parametric metric space, which is a generalized concept of parametric metric space. After that, the discussion is concerned with the existence of fixed points of single and multivalued maps on E -parametric metric spaces satisfying some contractive inequalities defined by an auxiliary function. [ABSTRACT FROM AUTHOR]

In this paper, the notion of sequential ς p -metric spaces has been introduced as a generalization of usual S -metric spaces, S b -metric spaces, S J S metric spaces, and specially of S p -metric spaces. In view of this notion, we prove some fixed point theorems for some classes of ς p -rational Geraghty JS-contractions over such spaces. A supporting example and an application have been given in order to examine the validity of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, the concept of sequential F -metric spaces has been introduced as a generalization of usual metric spaces, b -metric spaces, J S -metric spaces, and mainly F -metric spaces. Some topological properties of such spaces have been discussed here. By considering this notion, we prove fixed-point theorems for some classes of contractive mappings over such spaces. Examples have been given in order to examine the validity of the underlying space and in support of our fixed-point theorems. Moreover, our fixed-point theorem is applied to obtain solution of a system of linear algebraic equations. [ABSTRACT FROM AUTHOR]

Our aim is to establish a tripled fixed and coincidence point result on generalized C ∗ -algebra-valued metric spaces. We present an example on matrices. At the end, we give an application on integral equations. [ABSTRACT FROM AUTHOR]

In this paper, the concept of sequential p -metric spaces has been introduced as a generalization of usual metric spaces, b -metric spaces and specially of p -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems. [ABSTRACT FROM AUTHOR]

Ćirić and Prešić developed the concept of Prešić contraction to Ćirić-Prešić type contractive mappings in the background of a metric space. On the other hand, Altun and Olgun introduced Perov type F-contractions. In this paper, we extend the concept of Ćirić-Prešić contractions to Perov-Ćirić-Prešić type F-contractions. Our results modify some known ones in the literature. To support our main result, an example and an application to nonlinear operator systems are presented. [ABSTRACT FROM AUTHOR]

Ćirić and Prešić developed the concept of Prešić contraction to Ćirić-Prešić type contractive mappings in the background of a metric space. On the other hand, Altun and Olgun introduced Perov type F-contractions. In this paper, we extend the concept of Ćirić-Prešić contractions to Perov-Ćirić-Prešić type F-contractions. Our results modify some known ones in the literature. To support our main result, an example and an application to nonlinear operator systems are presented. [ABSTRACT FROM AUTHOR]

In this paper, first, we introduce the class of α φ − ω -Meir–Keeler contractive mappings and establish some fixed point results. Next, we introduce the notion of partial modular metric space and establish some fixed point results in this new spaces. As consequences of these results, we deduce some fixed point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. Some examples are furnished to demonstrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, we establish some new results on Jungck-Ćirić-Wardowski type mappings in complete metric spaces. Using our new approach, the conditions (W2) and (W3) of Wardowski do not apply for the proof of Cauchyness of the Picard-Jungck sequence. Our results generalize, improve and complement several results in the existing literature. [ABSTRACT FROM AUTHOR]

We introduce some generalizations of contractions for multi-valued mappings and establish some fixed point theorems for multi-valued mappings in b -metric spaces. Our results generalize and extend several known results in b-metric spaces. Some examples are included which illustrate the cases when new results can be applied while old ones cannot. [ABSTRACT FROM AUTHOR]

In this article, we obtain fixed point results under some rational contractive conditions for mappings in the setup of ordered ρ-metric spaces. Also, three examples and an application to existence of local solutions for first-order periodic problems are provided to illustrate the results presented herein. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coincidence point theorems for weakly-α-admissible contractive mappings in an extended b-metric space. Examples are provided to illustrate the usability of the obtained results. Our results generalize the results of several papers from metric and b-metric framework to the setting of extended b-metric spaces. [ABSTRACT FROM AUTHOR]

We extend some fixed point results for multi-valued F-contractions to multi-valued F-G-contractions. Motivated by the recent work of Ahmad et al. [Fixed point theory Appl., (2015) 2015:80] we define a new class of functions M(S; T) for two multi-valued mappings S and T and prove some fixed and common fixed point results for multi-valued F-G-contractions of Hardy-Rogers type. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of control functions and the concept of α-Θ-generalized Hardy-Rogers contraction and establish some fixed point results in the setting of b-metric spaces. Our results generalize many famous fixed point results such as Banach Contraction principle. Highlighting the obtained results, we present some illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of partial rectangular b-metric spaces and extend the concept of ĆiriĆ-PresiĆ first to Wardowski-ĆiriĆ-PresiĆ and then to J-S-ĆiriĆ-PresiĆ contractive mappings and obtain some fixed point theorems in this new class of generalized metric spaces. Our results generalize some results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some fixed point results for generalized Wardowski-type contractions in the framework of (α,η)-complete rectangular b-metric spaces. We also derive certain fixed point results for generalized F-contractions in rectangular b-metric spaces endowed with a graph or a partial order. Moreover, an illustrative example is presented to support the obtained results. [ABSTRACT FROM AUTHOR]

We introduce new concepts of generalized contractive and generalized α-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ćirić, Chatterjea, Kannan and Reich. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $(\alpha,\theta,k)$-contraction multi-valued mappings and establish some fixed point results for such mappings by using some control functions due to Jleli et al. (J. Inequal. Appl. 2014:439, 2014) in metric spaces and furnish some interesting examples to illustrate our main results. Also, we give some fixed point results in metric spaces endowed with a graph. Our results generalize and extend recent results given by some authors. [ABSTRACT FROM AUTHOR]

Considering α-admissible mappings in the setup of partial b-metric spaces, we establish some fixed and common fixed point results for ordered cyclic weakly (ψ, ϕ, L, A, B)-contractive mappings in complete ordered partial b-metric spaces. Our results extend several known results in the literature. Examples are also provided in support of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some common fixed point theorems for g-weakly isotone increasing mappings satisfying a generalized contractive type condition under a continuous function in the framework of ordered b-metric spaces. Our results extend the results of Nashine et al. [H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling 54 (2011) 712-720] from the context of ordered metric spaces to the setting of ordered b-metric spaces. Moreover, some examples of applications of the main result are given. Finally, we establish an existence theorem for a solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions of GP-metric space and GP (Λ;Θ)-contractive mapping and then prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach contraction principle to GP-metric spaces. An example shows the usefulness of our results. c 2014 All rights reserved. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define weak α-ψ-φ-contractive mappings and to establish coupled and tripled coincidence point theorems for such mappings defined on Gb-metric spaces using the concept of rectangular G-α-admissibility. As an application, we derive new coupled and tripled coincidence point results for weak ψ-φ-contractive mappings in partially ordered Gb-metric spaces. Our results are generalizations and extensions of some recent results in the literature. We also present an example as well as an application to nonlinear Fredholm integral equations in order to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

Using the concepts of G-metric, partial metric, and b-metric spaces, we define a new concept of generalized partial G-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this work, we obtain some fixed point results for generalized weakly T-Chatterjea-contractive and generalized weakly T-Kannan-contractive mappings in the framework of complete b-metric spaces. Examples are provided in order to distinguish these results from the known ones. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce the concept of N b -cone metric spaces over a Banach algebra as a generalization of N -cone metric spaces over a Banach algebra and b-metric spaces. Also, we study some coupled common fixed point theorems for generalized Lipschitz mappings in this framework. Finally, we give an example and an application to the existence of solutions of integral equations to illustrate the effectiveness of our generalizations. Some results in the literature are special cases of our results. [ABSTRACT FROM AUTHOR]

In this paper, we extend Darbo's fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the F -contractive condition in the framework of α − ν -complete modular b-metric spaces. Some results in ordered modular b-metric spaces are also presented. Moreover, an illustrative example and some related applications are presented to support the obtained results. [ABSTRACT FROM AUTHOR]

In [Fixed Point Theory Appl., 2015 (2015):185], the authors introduced a new concept of modified contractive mappings, generalizing Ćirić, Chatterjea, Kannan, and Reich type contractions. They applied the condition (θ 4) (see page 3, Section 2 of the above paper). Later, in [Fixed Point Theory Appl., 2016 (2016):62], Jiang et al. claimed that the results in [Fixed Point Theory Appl., 2015 (2015):185] are not real generalizations. In this paper, by restricting the conditions of the control functions, we obtain a real generalization of the Banach contraction principle (BCP). At the end, we introduce a weakly JS-contractive condition generalizing the JS-contractive condition. [ABSTRACT FROM AUTHOR]

The aim of this work is to extend the Mizoguchi-Takahashi fixed point result motivated by the approach of Wardowski (2012) and provide some related fixed point results in (ordered) metric spaces. An example is given to support the main results. Moreover, we provide an application on nonlinear differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we present the concept of Θ − (σ , ξ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results. [ABSTRACT FROM AUTHOR]

In this paper, motivated by the recent work [Journal of Nonlinear Sciences and Applications, 10(4):1544-1537] some generalized nonlinear contractive conditions via implicit functions and a-admissible pairs of multi-valued mappings in the setting of b-metric like spaces have been introduced. Some common fixed point results for such mappings in this framework have been provided. Then, some corollaries and consequences for our obtained results are given. Our results are the multi-valued versions of [Journal of Nonlinear Sciences and Applications, 10(4):1544-1537]. An example also is provided to support our obtained results. The presented results generalize and extend some earlier results in the literature. [ABSTRACT FROM AUTHOR]