Frum-Ketkov type multivalued operators

Let (M,d) be a metric space, X\subset M be a nonempty closed subset and K\subset M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F:X\to P(X) is said to be a strong Frum-Ketkov type operator if there exists \alpha\in ]0,1[ such that e_d(F(x),K)\le \alpha D_d(x,K), for every x\in X, where e_d is the excess functional generated by d and D_d is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators.

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A fixed point theorem for nonexpansive compact self-mapping

Annales Universitatis Mariae Curie-Sklodowska sectio A – Mathematica ◽

10.2478/umcsmath-2014-0005 ◽

2014 ◽

Vol 68 (1) ◽

Author(s):

T. D. Narang

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Topological Space ◽

Fixed Points ◽

Compact Subset ◽

Metric Space ◽

Closed Subset ◽

Continuous Family ◽

Underlying Space ◽

The Subject

AbstractA mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject

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Saturated contraction principles for non self operators, generalizations and applications

Filomat ◽

10.2298/fil1711391b ◽

2017 ◽

Vol 31 (11) ◽

pp. 3391-3406 ◽

Cited By ~ 1

Author(s):

Vasile Berinde ◽

Ştefan Măruşter ◽

Ioan Rus

Keyword(s):

Fixed Point ◽

Metric Space ◽

Closed Subset ◽

Unique Fixed Point ◽

Fixed Point Problem ◽

Point Problem ◽

Nonempty Closed Subset ◽

Open Problems ◽

Displacement Condition ◽

Well Posed

Let (X; d) be a metric space, Y ? X a nonempty closed subset of X and let f : Y ? X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator f has a unique fixed point; 2. The operator f satisfies a retraction-displacement condition; 3. The fixed point problem for f is well posed; 4. The operator f has the Ostrowski property. Some applications and open problems related to these questions are also presented.

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Fixed points of non-self almost contractions

Carpathian Journal of Mathematics ◽

10.37193/cjm.2014.01.02 ◽

2014 ◽

Vol 30 (1) ◽

pp. 7-14

Author(s):

MARYAM A. ALGHAMDI ◽

◽

VASILE BERINDE ◽

NASEER SHAHZAD ◽

◽

...

Keyword(s):

Boundary Condition ◽

Fixed Point ◽

Fixed Point Theorem ◽

Fixed Points ◽

Metric Space ◽

Closed Subset ◽

Fixed Point Theorems ◽

Fixed Point Theory ◽

Point Theory ◽

Convex Metric Space

Let X be a convex metric space, K a non-empty closed subset of X and T : K → X a non-self almost contraction. Berinde and Pacurar [Berinde, V. and P ˘ acurar, M., Fixed point theorems for nonself single-valued almost contractions, Fixed Point Theory, 14 (2013), No. 2, 301–312], proved that if T has the so called property (M) and satisfies Rothe’s boundary condition, i.e., maps ∂K (the boundary of K) into K, then T has a fixed point in K. In this paper we observe that property (M) can be removed and, hence, the above fixed point theorem takes place in a different setting.

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Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/auom-2019-0001 ◽

2019 ◽

Vol 27 (1) ◽

pp. 5-33 ◽

Cited By ~ 1

Author(s):

Hanan Alolaiyan ◽

Basit Ali ◽

Mujahid Abbas

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Space ◽

Hausdorff Distance ◽

Existence And Uniqueness ◽

Asymptotic Estimate ◽

Metric Spaces ◽

Multivalued Operators ◽

Fixed Point Sets

Abstract The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved.

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Generalized Spectral Theory in Complex Banach Algebras

Canadian Journal of Mathematics ◽

10.4153/cjm-1985-066-3 ◽

1985 ◽

Vol 37 (6) ◽

pp. 1211-1236

Author(s):

G. N. Hile ◽

W. E. Pfaffenberger

Keyword(s):

Banach Algebra ◽

Unit Circle ◽

Compact Subset ◽

Spectral Theory ◽

Complex Plane ◽

Banach Algebras ◽

Complex Banach Algebra ◽

Nonempty Compact ◽

Nonempty Compact Subset

Let A be an element of a complex Banach algebra with identitI. The ordinary spectrum of A, sp(A), consists of those points z in the complex plane such that A — zI has no inverse in . If Q is any other element of , we define spQ(A), the spectrum of A relative to Q, or Q-spectrum of A, as those points z such that has no inverse in . Thus if Q = 0 the Q-spectrum of A is the same as the ordinary spectrum of A.The generalized notion of spectrum, spQ(A), retains many of the properties of the ordinary spectrum, particularly when A and Q commute and the ordinary spectrum of Q does not meet the unit circle. Under these conditions the Q-spectrum of A is a nonempty compact subset of the plane, and if both sp(A) and sp(Q) are finite (or countable), so is spQ(A).

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Asymptotic behavior of inexact infinite products of nonexpansive mappings

Studia Universitatis Babes-Bolyai Matematica ◽

10.24193/subbmath.2021.1.12 ◽

2021 ◽

Vol 66 (1) ◽

pp. 127-138

Author(s):

Simeon Reich ◽

Alexander J. Zaslavski

Keyword(s):

Asymptotic Behavior ◽

Metric Space ◽

Closed Subset ◽

Complete Metric Space ◽

Nonexpansive Mappings ◽

Nonempty Closed Subset ◽

Infinite Products

"We analyze the asymptotic behavior of inexact infinite products of nonexpansive mappings, which take a nonempty closed subset of a complete metric space into the space, in the case where the errors are sufficiently small."

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

Filomat ◽

10.2298/fil1711157a ◽

2017 ◽

Vol 31 (11) ◽

pp. 3157-3172

Author(s):

Mujahid Abbas ◽

Bahru Leyew ◽

Safeer Khan

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Periodic Solutions ◽

Metric Space ◽

Delay Differential Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Existence Of Periodic Solutions ◽

Delay Differential

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.

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Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽

10.3390/sym13030501 ◽

2021 ◽

Vol 13 (3) ◽

pp. 501

Author(s):

Ahmed Boudaoui ◽

Khadidja Mebarki ◽

Wasfi Shatanawi ◽

Kamaleldin Abodayeh

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Metric Space ◽

Fixed Point Theorems ◽

Coupled Fixed Point ◽

Sufficient Conditions ◽

Impulsive Differential Equations ◽

System Of Differential Equations ◽

Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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Hybrid fixed points of multivalued operators in metric spaces with applications

Nonlinear Analysis ◽

10.1016/j.na.2008.08.020 ◽

2009 ◽

Vol 70 (11) ◽

pp. 4106-4117 ◽

Cited By ~ 10

Author(s):

Shihuang Hong ◽

Dongxue Guan ◽

Li Wang

Keyword(s):

Fixed Points ◽

Metric Spaces ◽

Multivalued Operators

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Fixed point theorems for expansive mappings in Gp-metric spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2017.03.07 ◽

2017 ◽

Vol 26 (3) ◽

pp. 297-308

Author(s):

MELTEM KAYA ◽

◽

HASAN FURKAN ◽

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Partial Metric ◽

Expansive Mapping ◽

Partial Metric Spaces ◽

Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

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