Family Of Self-mappings Research Articles

Common Fixed Point Theorems for Commuting Self Maps in Banach Spaces via a Measure of Non-compactness

This paper provides common fixed point theorems for a commuting family of self mappings in Banach spaces via a measure of non-compactness. The choice of a commuting family of self maps provides a result that is unique in its own right, generalize Darbos fixed point theorem and specifically extend and improve the work of Meryeme El Harrak and Ahmed Hajji.

(F, L) Contractions on Complete Weak Partial Metric Spaces for a Commuting Family of Self Mappings

The aim of this paper is to clarify the choice of the self map T : X → X in Kaya et als (F,L) weak contractions by choosing a family Tn, n ∈ N of (F,L) contractions. Motivated by the fact that the uniform limit T of the family of self maps is a better approximation, we are guaranteed the choice of the self map. By this, the choice of T is no longer arbitrary. Again, for any nite family T1, T2, T3, · · · , TN of (F,L) contractions their composition is an (F,L) contraction. This concept generalizes and improves on several results especially Theorems 3.1 and 3.2 of [10].

Skew ring extensions and generalized monoid rings

A D-structure on a ring A with identity is a family of self-mappings indexed by the elements of a monoid G and subject to a long list of rather natural conditions. The mappings are used to define a generalization of the monoid algebra A[G]. We consider two of the simpler types of D-structure. The first is based on a homomorphism from G to End(A) and leads to a skew monoid ring. We also explore connections between these D-structures and normalizing and subnormalizing extensions. The second type of D-structure considered is built from an endomorphism of A. We use D-structures of this type to characterize rings which can be graded by a cyclic group of order 2.

Metric type spaces and λ-sequences

In this article, we introduce the concept of λ-sequences in a metric type space. We give a general overview of the concept and use it to prove the existence of common fixed points for a family of self mappings defined on a metric type space.

Implicit relations related to ordered orbitally complete metric spaces and applications

In this study, the notions of asymptotically regular mappings and orbitally continuity are used to prove common fixed point results for four mappings satisfying an implicit relation involving a control function on an ordered orbitally complete metric space. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. We furnish suitable examples to demonstrate the validity of the hypotheses of our results which can fail if some of these condition is missing. It is also verified that the proposed results have an important role to derive applications to certain systems of integral equations. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

Common fixed point theorems for infinite families of contractive maps

In this paper, we prove some fixed point theorems for infinite families of self-mappings of a complete metric space satisfying some new conditions of common contractivity. An example is presented to show the effectiveness of our results.

SOME FIXED POINT THEOREMS VIA COMMON LIMIT RANGE PROPERTY IN NON-ARCHIMEDEAN MENGER PROBABILISTIC METRIC SPACES

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized -contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

COMMON FIXED POINT THEOREM FOR A PAIR OF WEAKLY COMPATIBLE SELF-MAPPINGS IN FUZZY METRIC SPACE USING (CLRG) PROPERTY

In this paper we prove a common fixed point theorem for a pair of weakly compatible self-mappings in fuzzy metric space by using (CLRg) property. The result is extended for two finite families of self-mappings in fuzzy metric space by using the concept of pairwise commuting. An example is provided which demonstrates the validity of main theorem.

Fixed Points of Weakly Compatible Mappings Satisfying Generalized $$\varphi $$ φ -Weak Contractions

In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a \(\varphi \)-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature.

Some integral type common fixed point theorems satisfying $\phi$-contractive conditions

In this manuscript, we obtain some common fixed point results of two pairs having the common limit range property in the setting of integral type contraction in the framework of symmetric (semi-metric) spaces. Moreover, we extend our results from two pairs of self-mappings to four finite families of self mappings to get common fixed points. Our results improve and extend a host of previously known results. Further, we establish some illustrative examples to show the validity of the main results.

Unified fixed point theorems for mappings in fuzzy metric spaces via implicit relations

Abstract In this paper, we prove some fixed point theorems for weakly compatible mappings in fuzzy metric spaces employing common limit range property with implicit relations. We also furnish some illustrative examples to support our main results. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Gopal et al. (2011).

Some Fixed Point Results for a Sequence of Mappings on G‐Metric Space

AbstractIn the setting of generalized metric spaces, so called G‐metric spaced introduced by Z. Mustafa and B. Sims in 2006, some fixed point results for mappings with contractive iterate at a point and common fixed point results for infinite family of self mappings will be presented. The results are generalizations of well known results in the metric space. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Existence and uniqueness of a common fixed point under a limit contractive condition

Abstract In this paper, utilizing the notion of common limit range property for two pairs of self mappings, we prove common fixed point theorems in fuzzy metric spaces under a limit contractive condition, which improve and extend the results of Zhu et al. [Common fixed point theorems of new contractive conditions in fuzzy metric spaces, J. Appl. Math. 2013:145190, 2013]. We also give some examples to demonstrate the validity of the hypotheses of our results. As an application to our main result, we obtain a fixed point theorem for four finite families of self mappings in fuzzy metric space. MSC: 47H10, 54H25.

Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dynamic programming

In this paper, we prove some integral type common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are furnished which demonstrate the validity of our results. We extend our main result to four finite families of self-mappings employing the notion of pairwise commuting. Moreover, we give an application which supports the usability of our main theorem.

Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces

The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed points in modified intuitionistic fuzzy metric spaces enjoying an implicit function utilized in Tanveer et al. (2012) and Imdad et al. (2012). As an application to our main result, we derive a fixed point theorem for finite families of self-mappings. We also give some examples which demonstrate the validity of the hypotheses and degree of generality of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature.

FIXED POINT THEOREMS IN NON-ARCHIMEDEAN MENGER PM-SPACES USING COMMON PROPERTY (E.A)

In this paper, we prove common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are derived which demonstrate the validity of our results. As an application to our main result, we present a fixed point theorem for four finite families of self mappings. Our results improve and extend several existing results in the literature.

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces

In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} ieN in 2-metric space have an unique common fixed point if 1) {Ti,j} ieN satisfies Φj-contractive condition, where ΦjeΦ, for each jeN ; 2) Tm,μ n,v for all m,n,μ,veN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.

Unique common fixed point of a family of self-maps with same type contractive condition in 2-metric space

In this paper, we prove that a family of self-maps {Ti, j}i, j∈ℕ in 2-metric space has a unique common fixed point if (i) {Ti, j}i, j∈ℕ satisfies the same type contractive condition for each j ∈ ℕ; (ii) Tm, μ ·Tn, ν = Tn, ν · Tm, μ for all m, n, μ, ν ∈ ℕ with μ ≠= ν. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.