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In this paper, f-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional Φ-comparison functions in fuzzy metric spaces. Next, generalized f-contractions are defined by using five-dimensional Φ-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper we will extend the concept of multi-valued Feng--Liu contraction, by imposing a nonlinear assumption on the operator. Then, fixed point, strict fixed point and stability theorems for the fixed point inclusion with multi-valued nonlinear Feng--Liu contractions are given. An application illustrates the main theoretical results. [ABSTRACT FROM AUTHOR]

One of the important consequences of the Banach fixed point theorem is Hutchinson's theorem which states the existence and uniqueness of fractals in complete metric spaces. The aim of this paper is to extend this theorem for semimetric spaces using the results of Bessenyei and Páles published in 2017. In doing so, some properties of semimetric spaces as well as of the fractal space are investigated. We extend Hausdorff's theorem to characterize compactness and Blaschke's theorems to characterize the completeness of the fractal space. Based on these preliminaries, an analogue of Hutchinson's theorem in the setting of semimetric spaces is proved, and finally, error estimates and stability of fractals are established as well. [ABSTRACT FROM AUTHOR]

In this paper, we point out an error in proving famous Achari type nonunique fixed point results. Also, we prove some best proximity point results in b -metric spaces by introducing new concepts. Hence, we develop some results existing in the literature. Finally, we give a result for the existence of the solution of nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this paper is to obtain fixed points of Ćirić type operators in the framework of extended b-metric space introduced by Kamran et al. (Mathematics 5:19, 2017). Our results unify and improve the results of Alqahtani et al. (Mathematics 6:68, 2018), Alsulami et al. (Filomat 3(11): 3147–3156, 2017) and others. As an application of our result, we establish an existence of solution of nonlinear Fredholm integral equation. A numerical example is also presented to support our result. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to establish some new results about the existence and uniqueness for coincidence problems for two single-valued mappings. Moreover, we present some applications of our results to the existence and uniqueness of solutions of some boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the setting of multiplicative metric spaces to establish results regarding the common fixed points of four mappings, using a contraction condition defined by means of a comparison function. Also, we provide illustrative examples in support of our new results. The results obtained in this paper extend and improve some well-known comparable results in the literature due to He et al. (Fixed Point Theory and Appl. 2013:48, 2013). [ABSTRACT FROM AUTHOR]

In this paper we prove some theorems in quasi{cone metric space relating to the diameter of orbits by using a comparison function, which generalize the results of Babu [2] and Jachymski [6] and many others. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a fixed point theorem for mappings satisfying cyclic φ-contractive conditions in complete metric spaces, which gives a positive answer to the question raised by Radenović (Fixed Point Theory Appl. 2015:189, ). We also find that this result and the fixed point result satisfying cyclic weak ϕ-contractions given by Karapınar (Appl. Math. Lett. 24:822-825, ) are independent of each other. Furthermore, when the number of cyclic sets is odd, we obtain fixed point theorems satisfying cyclic weak ϕ-contractions and cyclic φ-contractions in the setting of generalized metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider, discuss, improve, and complement recent fixed points results for mappings satisfying cyclical contractive conditions established by Pacurar and Rus (Nonlinear Anal. 72:1181-1187, 2010) and Chandok and Postolache (Fixed Point Theory Appl. 2013:28, 2013). By using a new lemma we get much shorter and nicer proofs of some results with the new concept of mappings. [ABSTRACT FROM AUTHOR]

In this paper, φ-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized φ-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.

In this paper, we will present some fixed set and fixed point theorems for nonself multivalued generalized contractions. We will discuss the cases of multivalued contractions, multivalued φ-contractions and multivalued Kannan contractions. Our results propose some existence, uniqueness and related properties of the multivalued fractal generated by iterative multifunction systems. The approach is based on some new properties proved for the multi-fractal operator induced by a nonself multivalued generalized contraction. Some open problems are also formulated. [ABSTRACT FROM AUTHOR]

Copyright of Kuwait Journal of Science is the property of Kuwait University, Academic Publication Council and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we use the concept of C-class functions introduced by Ansari [4] to prove the existence and uniqueness of common fixed point for self-mappings in modular spaces of integral inequality. Our results extended and generalized previous known results in this direction. [ABSTRACT FROM AUTHOR]

In this study, we characterize a novel contraction mapping referred to as αji-(DC (PE))-contraction in light of DC-contraction mappings associated with the Geraghty-type contraction and E-type contraction. Besides, a novel common fixed-point theorem providing such mappings is demonstrated in the context of partial b-metric spaces. It is stated that the main theorem is a generalization of the existing literature, and its comparisons with the results are expressed. Additionally, the efficiency of the result of this study is demonstrated through some examples and an application to homotopy theory. [ABSTRACT FROM AUTHOR]

In this paper, some coupled fixed point stability results for one and two metrics are obtained in complete metric spaces by using some general contractive conditions some of which involve comparison functions. Our results are generalizations and exten- sions of [M.O. Olatinwo: Some stability results in complete metric space, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 48(2009), 83-92] and [M.O. Olatinwo: Stability of coupled fixed point iterations and the continuous dependence of coupled fixed points, Comm. Appl. Nonlinear Anal., 19(2012), No. 2, 71-83] as well as some others in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of fixed points of rational type contractions in the setting of extended b-metric spaces. Our results extend considerably several well-known results in the existing literature. We present some nontrivial examples to show the validity of our results. Furthermore, as applications, we obtain the existence of solution to a class of Fredholm integral equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some best proximity results for multivalued cyclic operators satisfying a Ćirićtype condition. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we give a new proof of a result by S. Reich and A.J. Zaslavski (S. Reich and A.J. Zaslavski, A fixed point theorem for Matkowski contractions, Fixed Point Theory, 8(2007), No. 2, 303-307). Some new fixed point theorems for nonself generalized contractions are also given. [ABSTRACT FROM AUTHOR]

In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize many relevant results of the existing literature. Interestingly, unlike several other cases, our main results deduce a nonlinear order-theoretic version of a well-known fixed point theorem (proved for quasi-contraction) due to Ćirić (Proc. Amer. Math. Soc., 45(1974), 267-273). Finally, in the setting of metric spaces, we drive a sharpened version of Theorem 1 due to Berinde and Vetro (Fixed Point Theory Appl., 2012, 2012:105, 8 pages). [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of Λ , Υ , ℜ -contraction mappings under the effect of comparison functions and an arbitrary binary relation. We establish related common fixed point theorems. We explain the significance of our main theorem through examples and an application to a solution for the following nonlinear matrix equations: X = D + ∑ i = 1 n A i ∗ X A i − ∑ i = 1 n B i ∗ X B i X = D + ∑ i = 1 n A i ∗ γ X A i , where D is an Hermitian positive definite matrix, A i , B i are arbitrary p × p matrices and γ : H (p) → P (p) is an order preserving continuous map such that γ (0) = 0 . A numerical example is also presented to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

We introduce Jc‐contraction, which encompasses both F‐contraction and JS‐contraction. We investigate a fixed‐point problem subject to Jc‐contraction. The existence of the solutions to the linear matrix equation and system of fractional differential equations are discussed by the application of obtained results. [ABSTRACT FROM AUTHOR]

This paper discusses approximation of semigroups of locally Lipschitz operators by discrete semigroups of local quasi-contractions with respect to metric-like functionals. The main approximation result not only extends a product formula for contractive semigroups generated by maximal dissipative operators in real Hilbert spaces but also gives an algorithm for solving a mixed problem for the Kirchhoff equation to which the contractive semigroup theory or Kato's quasilinear theory cannot directly apply. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of fixed points of rational type contractions in the setting of extended b-metric spaces. Our results extend considerably several well-known results in the existing literature. We present some nontrivial examples to show the validity of our results. Furthermore, as applications, we obtain the existence of solution to a class of Fredholm integral equations.

In this paper, we introduce a new large contraction via (c)-comparison function in the setting of complete metric space. We investigate the existence of a fixed point for such contractions.

In this paper, we study the behavior of Λ , Υ , ℜ -contraction mappings under the effect of comparison functions and an arbitrary binary relation. We establish related common fixed point theorems. We explain the significance of our main theorem through examples and an application to a solution for the following nonlinear matrix equations: X = D + ∑ i = 1 n A i ∗ X A i − ∑ i = 1 n B i ∗ X B i X = D + ∑ i = 1 n A i ∗ γ X A i , where D is an Hermitian positive definite matrix, A i , B i are arbitrary p × p matrices and γ : H ( p ) → P ( p ) is an order preserving continuous map such that γ ( 0 ) = 0 . A numerical example is also presented to illustrate the theoretical findings.

In this paper, we apply the concept of cyclic φ -contraction for presenting a fixed point theoremon a Hausdorff uniform space.