scholarly journals Diametrically contractive mappings

2004 ◽  
Vol 70 (3) ◽  
pp. 463-468 ◽  
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Compact Subset ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
Weakly Compact ◽  
Contractive Mappings

A contractive mapping on a complete metric space may fail to have a fixed point. Diametrically contractive mappings are introduced and it is shown that a diametrically contractive self-mapping of a weakly compact subset of a Banach space always has a fixed point.

scholarly journals Fuzzy Fixed Point Results For Φ Contractive Mapping with Applications

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
G. N. V. Kishore
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contractive Mapping ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Control Functions ◽  
Complex Valued Metric Space ◽  
Fuzzy Fixed Point ◽  
Complex Valued ◽  
Rational Type

In this paper, using rational type contractions, common fuzzy fixed point result for Φ contractive mappings involving control functions as coefficients of contractions in the setting of complex-valued metric space is established. The derived results generalizes some result in the existing literature. To show the validity of the derived results an appropriate example and applications are also discussed.

scholarly journals SOLVABILITY OF THE CAUCHY PROBLEM FOR EQUATIONS WITH RIEMANN–LIOUVILLE’S FRACTIONAL DERIVATIVES

2018 ◽  
Vol 62 (4) ◽  
pp. 391-397 ◽  
Author(s):  
Petr P. Zabreiko ◽  
Svetlana V. Ponomareva
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Fixed Point ◽  
Unique Solution ◽  
Metric Space ◽  
Fractional Derivatives ◽  
Volterra Equation ◽  
Complete Metric Space ◽  
The Cauchy Problem ◽  
The Right

In this article we study the solvability of the analogue of the Cauchy problem for ordinary differential equations with Riemann–Liouville’s fractional derivatives with a nonlinear restriction on the right-hand side of functions in certain spaces. The conditions for solvability of the problem under consideration in given function spaces, as well as the conditions for existence of a unique solution are given. The study uses the method of reducing the problem to the second-kind Volterra equation, the Schauder principle of a fixed point in a Banach space, and the Banach-Cachoppoli principle of a fixed point in a complete metric space.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

scholarly journals ON Modified(α-η)-Contractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Muhammad Arshad ◽  
Aftab Hussain
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Contractive Mappings

Hussain et al. (2013) established new fixed point results in complete metric space. In this paper, we prove fixed point results ofα-admissible mappings with respect toη, for modified contractive condition in complete metric space. An example is given to show the validity of our work. Our results generalize/improve several recent and classical results existing in the literature.

scholarly journals Existence of common fixed points of non-linear semigroups of Enriched Kannan contractive mappings

2021 ◽  
Vol 38 (1) ◽  
pp. 169-178
Author(s):  
SAYANTAN PANJA ◽  
◽  
MANTU SAHA ◽  
RAVINDRA K. BISHT ◽  
◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Banach Space ◽  
Normal Structure ◽  
Contractive Mapping ◽  
Common Fixed Points ◽  
Contractive Mappings ◽  
Non Linear

In this article, we consider the non-linear semigroup of \textit{enriched Kannan} contractive mapping and prove the existence of common fixed point on a non-empty closed convex subset $\mathcal C$ of a real Banach space $\mathscr X$, having uniformly normal structure.

scholarly journals Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

2021 ◽  
Vol 2106 (1) ◽  
pp. 012015
Author(s):  
A Wijaya ◽  
N Hariadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
C Algebra ◽  
Metric Function ◽  
Interesting Theorem

Abstract Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

scholarly journals Stability of Picard operators under operator perturbations

2018 ◽  
Vol 56 (2) ◽  
pp. 3-12
Author(s):  
Adrian Petruşel ◽  
Ioan A. Rus
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
Picard Operator

AbstractIn this paper we study the following problems: I. Let (M, d) be a complete metric space and f, g : M → M be two operators. We suppose that:(a) f is a Picard operator with its unique fixed point x *f;(b) there exists η > 0 such that d(f(x), g(x)) ≤ η, for every x ∈ M.The problem consists in estimating d(gn(x), x*f), for x ∈ M and n ∈ 𝕅*.II. Let B be a Banach space and f, g : B → B be two operators. We suppose that f is a Picard operator. The problem is to find sufficient conditions which guarantee that f + g is a Picard operator.

scholarly journals Endpoints of φ-weak and generalized φ-weak contractive mappings

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 725-732 ◽  
Author(s):  
Sirous Moradi ◽  
Farshid Khojasteh
Keyword(s):  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
Contractive Mappings

Let (X, d) be a complete metric space, and let T:X ? Pd,bd (X) be a multi-valued ?-weak or generalized ?-weak contractive mapping. Then T has a unique endpoint if and only if T has the approximation endpoints property. Our results extend previous results given by Ciric(1974), Nadler (1969), Daffer-Kaneko (1995), Rhoades (2001), Rouhani and Moradi (2010), Amini-Harandi (2010) and Moradi and Khojasteh (2011).

On Fixed Point Theorems in Complete Metric Space

2019 ◽  
Vol 10 (7) ◽  
pp. 1419-1425
Author(s):  
Jayashree Patil ◽  
Basel Hardan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space

Some fixed point results for (β-ψ1-ψ2)-contractive conditions in ordered b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Altering Distance

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.

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