Generalization Of Fixed Point Theorem Research Articles

Fixed point theorems of generalized Gregus type in quasi-metric spaces for two pairs of mappings satisfying common coincidence range property

The purpose of this paper is to prove some general fixed point theorems for two pairs of mappings satisfying implicit relations of generalized Gregus type in quasi-metric spaces without the notion of sequence and inequality. As applications we obtain new results for mappings satisfying contractive / extensive conditions of integral type and in G-metric spaces.

Some general fixed point theorems on topological vector spaces

Some general fixed point theorems on topological vector spaces

A fixed point theorem for mappings satisfying a new common range property

In this paper a general fixed point theorem for two pairs of mappings satisfying a new type of common range property without limit of sequences in metric spaces are proved.

Asymptotic problems for functional differential equations via linearization method

We study the existence of positive decreasing solutions (the so-called Kneser solutions) for a class of second-order functional differential equations with a damping term. A linearization approach based on a general fixed point theorem is used to achieve this goal. The existence of zero-decaying Kneser solutions is also proved. Finally, the role of the deviating argument to the asymptotic behavior of solutions is illustrated together with some discrepancies between equations with or without delay.

Fixed Point Theorems for Two Pairs of Mappings Satisfying a New Type of Common Limit Range Property in Gp Metric Spaces

Abstract The purpose of this paper is to prove a general fixed point theorem for mappings involving almost altering distances and satisfying a new type of common limit range property in Gpmetric spaces. In the last part of the paper, some fixed point results for mappings satisfying contractive conditions of integral type and for ⱷ-contractive mappings are obtained.

Fixed Point Theorems for Monotone Caristi Inward Mappings

In this paper, we introduce the monotone Caristi inward mappings. As an example, we show that monotone inward contraction mappings are monotone Caristi inward mappings. A general fixed point theorem for such mappings is given. A mutlivalued version of these results is also introduced.

"A general fixed point theorem for mappings satisfying an implicit relation in complete Gp - metric spaces "

"A general fixed point theorem for mappings satisfying an implicit relation in complete Gp - metric spaces "

A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation

Abstract In this paper a general fixed point theorem for mappings with a new type of common limit range property satisfying a mixed implicit relation is proved. In the last part of the paper, as application, some fixed point results for mappings satisfying contractive conditions of integral type and for φ-contractive mappings are obtained.

The Knaster–Tarski theorem versus monotone nonexpansive mappings

Let $X$ be a partially ordered set with the property that each family of order intervals of the form $[a,b],[a,\rightarrow )$ with the finite intersection property has a nonempty intersection. We show that every directed subset of $X$ has a supremum. Then we apply the above result to prove that if $X$ is a topological space with a partial order $\preceq $ for which the order intervals are compact, $\mathcal{F}$ a nonempty commutative family of monotone maps from $X$ into $X$ and there exists $c\in X$ such that $c\preceq Tc$ for every $T\in \mathcal{F}$, then the set of common fixed points of $\mathcal{F}$ is nonempty and has a maximal element. The result, specialized to the case of Banach spaces gives a general fixed point theorem that drops almost all assumptions from the recent results in this area. An application to the theory of integral equations of Urysohn's type is also given.

Generalization of Fixed Point Theorems in Pseudocompact Tichonov Space

In this paper we study some fixed point results in pseudocompact Tichnovo space using Edelstein type contractive conditions. The results presented in this paper include the generalization of some fixed point theorems established by Fisher and Pathak.

FIXED POINT THEOREMS FOR TWO PAIRS OF MAPPINGS IN PARTIAL METRIC SPACES

In this paper, a general fixed point theorem for two pairs of weakly compatible mappings satisfying a - implicit relation different from the type from [16] is proved. As applications, we obtain the sufficient conditions for the existence of fixed points for a sequence of mappings in partial metric spaces.

A new Ф-generalized quasi metric space with some fixed point results and applications

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

A general fixed point theorem for two hybrid pairs of mappings satisfying a mixed implicit relation and applications

A general fixed point theorem for two hybrid pairs of mappings satisfying a mixed implicit relation and applications

Fixed point theorem of Ciric type in weak partialmetric spaces

In this paper we prove a general fixed point theorem of Ciric type in weak partial metric space.

Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property

The purpose of this paper is to prove a general fixed point theorem for mappings involving almost altering distances and satisfying a new type of common limit range property which generalize the results from Theorem 2.9 [19]. In the last part of the paper, as applications, some fixed point results for mappings satisfying contractive conditions of integral type for almost contractive mappings for ?-contractive mappings and (?,?) - weak contractive mappings in metric spaces are obtained.

A general fixed point theorem for a pair of multi-valued mappings in partial metric spaces

AbstractThe purpose of this paper is to prove a general fixed point theorem for a pair of multi-valued mappings satisfying a new type of implicit relation in partial metric spaces, which generalizes Theorem 2.2 [4], Theorem 3.1 [3], Theorem 3.2 [7], Corollary 2.3 [4], Theorem 2.8 [16] and obtain other particular results.

Two general fixed point theorems for a sequence of mappings satisfying implicit relations in Gp - metric spaces

<p>In this paper, two general fixed point theorem for a sequence of mappings satisfying implicit relations in Gp - complete metric spaces are proved.</p>

A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

Abstract In this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15], [13], [14], [16], [10] and from other papers, is proved.

WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES

The purpose of this paper is to prove a general fixed point theorem in Gp - metric space for mappings satisfying an implicit relation. If Gp - metric is symmetric, we prove that the fixed point problem is well posed.

Generalized Cauchy means

Given two means M and N, the operator \({\mathcal{M}_{M,N}}\) assigning to a given mean μ the mean $$\mathcal{M}_{M,N}(\mu )(x,y)=M(\mu (x,N(x,y)),\mu (N(x,y),y))$$was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation $$\mathcal{M}_{A_{(f)},A_{(g)}}(\mu )=\mu ,$$where A (f) and A (g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator \({\mathcal{M}_{M,N}}\) is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates \({\mathcal{M} _{M,N}^{n}}\). The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem.