scholarly journals A fixed point theorem for nonexpansive compact self-mapping

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

scholarly journals Fixed points of non-self almost contractions

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.

scholarly journals FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

2020 ◽  
pp. 283
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

scholarly journals Frum-Ketkov type multivalued operators

2021 ◽  
Vol 37 (2) ◽  
pp. 203-210
Author(s):  
ERDAL KARAPINAR ◽  
ADRIAN PETRUŞEL ◽  
GABRIELA PETRUŞEL
Keyword(s):  
Fixed Points ◽  
Compact Subset ◽  
Metric Space ◽  
Closed Subset ◽  
Type Operator ◽  
Multivalued Operator ◽  
Nonempty Closed Subset ◽  
Multivalued Operators ◽  
Nonempty Compact ◽  
Nonempty Compact Subset

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.

scholarly journals Unique Fixed Point Theorem for Weakly C-Contractive Mappings

1970 ◽  
Vol 5 (1) ◽  
pp. 6-13 ◽  
Author(s):  
Binayak S Choudhury
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Engineering And Technology ◽  
Existing Result

In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces. Key words: Metric space; Fixed point; Weak C-contraction. M S C (2000): 54H25   DOI: 10.3126/kuset.v5i1.2842 Kathmandu University Journal of Science, Engineering and Technology Vol.5, No.1, January 2009, pp 6-13

scholarly journals Common Fixed Points for Mappings under Contractive Conditions of (α,β,ψ)-Admissibility Type

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 261 ◽  
Author(s):  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Common Fixed Points ◽  
Common Fixed Point Theorem

In this paper, we introduce the notion of ( α , β , ψ ) -contraction for a pair of mappings ( S , T ) defined on a set X. We use our new notion to create and prove a common fixed point theorem for two mappings defined on a metric space ( X , d ) under a set of conditions. Furthermore, we employ our main result to get another new result. Our results are modifications of many existing results in the literature. An example is included in order to show the authenticity of our main result.

scholarly journals Fixed points of Kannan mappings in metric spaces endowed with a graph

2012 ◽  
Vol 20 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Florin Bojor
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces

AbstractLet (X; d) be a metric space endowed with a graph G such that the set V (G) of vertices of G coincides with X. We define the notion of G-Kannan maps and obtain a fixed point theorem for such mappings

scholarly journals Fixed points in k complete metric spaces

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Luljeta Kikina ◽  
Kristaq Kikina
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Spaces

AbstractA fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [

scholarly journals A Common Coincidence of Fixed Point for Generalized Caristi Fixed Point Theorem

2021 ◽  
Vol 2 (1) ◽  
pp. 40-46
Author(s):  
Jayashree Patil ◽  
Basel Hardan ◽  
Amol Bachhav
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Weakly Compatible

In this paper, the interpolative Caristi type weakly compatible contractive in a complete metric space is applied to show some common fixed points results related to such mappings. Our application shows that the function which is used to prove the obtained results is a bounded map. An example is provided to show the useability of the acquired results.

scholarly journals Alpha- F -Convex Contraction Mappings in b -Metric Space and a Related Fixed Point Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kitila Wirtu Geleta ◽  
Kidane Koyas Tola ◽  
Solomon Gebregiorgis Teweldemedhin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mappings

In this paper, we establish fixed point theorems for α - F -convex contraction mappings in b -metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.

scholarly journals A fixed point theorem for mappings satisfying a general contractive condition of integral type

2002 ◽  
Vol 29 (9) ◽  
pp. 531-536 ◽  
Author(s):  
A. Branciari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Fixed Points ◽  
Compact Subset ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Integrable Mapping

We analyze the existence of fixed points for mappings defined on complete metric spaces(X,d)satisfying a general contractive inequality of integral type. This condition is analogous to Banach-Caccioppoli's one; in short, we study mappingsf:X→Xfor which there exists a real numberc∈]0,1[, such that for eachx,y∈Xwe have∫0d(fx,fy)φ(t)dt≤c∫0d(x,y)φ(t)dt, whereφ:[0,+∞[→[0,+∞]is a Lebesgue-integrable mapping which is summable on each compact subset of[0,+∞[, nonnegative and such that for eachε>0,∫0εφ(t)dt>0.

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