scholarly journals Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12
Author(s):  
Reny George ◽  
Hemanth Kumar Pathak
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
The Other ◽  
Inclusion Problem ◽  
Integral Inclusion ◽  
New Variant ◽  
Multivalued Contractions ◽  
Filippov Type

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.

scholarly journals Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

scholarly journals Some fixed point theorems for Hardy-Rogers type mappings

1984 ◽  
Vol 7 (1) ◽  
pp. 75-87 ◽  
Author(s):  
B. E. Rhoades ◽  
S. Sessa ◽  
M. S. Khan ◽  
M. D. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
The Other

The first result establishes a fixed point theorem for three maps of a complete metric space. The contractive definition is a generalization of that of Hardy and Rogers, and the commuting condition of Jungck is replaced by the concept of weakly commuting. The other results are extensions of some theorems of Kannan.

scholarly journals Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 849 ◽  
Author(s):  
Pradip Debnath ◽  
Manuel de La de La Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Other

In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for set-valued Reich–Rus–Ćirić-type contractions. Examples are provided to validate the results.

New sufficient conditions for contractively widely more generalized hybrid mappings to have a fixed point

2016 ◽  
Vol 09 (04) ◽  
pp. 1650082
Author(s):  
Toshiharu Kawasaki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
The Other ◽  
Nonlinear Anal ◽  
Linear And Nonlinear

Hasegawa, Kawasaki and Kobayashi [Fixed point theorems for contractively widely more generalized hybrid mappings in metric spaces, to appear in Linear and Nonlinear Anal.] introduced the concept of contractively widely more generalized hybrid mappings in a metric space. On the other hand, Bogin [A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad. Math. Bull. 19 (1976) 7–12] showed a fixed point theorem. However, Bogin’s result is not included in our results. In this paper, we consider new sufficient conditions as to cover the Bogin’s fixed point theorem for contractively widely more generalized hybrid mappings to have a fixed point.

The existence theorem of a new multi-valued mapping in metric space endowed with graph

2017 ◽  
Vol 33 (2) ◽  
pp. 191-198
Author(s):  
ARAYA KHEAWBORISUT ◽  
◽  
SUTHEP SUANTAI ◽  
ATID KANGTUNYAKARN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Directed Graph ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Ordered Metric Spaces ◽  
New Type

In this paper, we introduce a new type of multi-valued G-contraction mapping on a metric space endowed with a directed graph G and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present.

scholarly journals Some Fixed Point Theorems in -Metric Space Endowed with Graph

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Maria Samreen ◽  
Tayyab Kamran ◽  
Naseer Shahzad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contraction Mappings ◽  
Cyclic Operators

We define some notions of contraction mappings in -metric space endowed with a graph and subsequently establish some fixed point results for such classes of contractions. According to the applications of our results, we obtain fixed point theorems for cyclic operators and an existence theorem for the solution of an integral equation.

scholarly journals Multivalued φ contractions and fixed point theorems

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1209-1220 ◽  
Author(s):  
Maria Samreen ◽  
Khansa Waheed ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Primary Structure ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Higher Order ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Integral Inclusion

In this paper we establish some fixed point theorems for multivalued mappings satisfying contractive condition involving gauge function when the underlying primary structure is b-metric space. Our proposed iterative scheme converges to the fixed point with higher order. Moreover, we also calculate priori and posteriori estimates for the fixed point. Our main results generalize/extend many perexisting results in literature. Consequently, to substantiate the validity of our result we obtain an existence result for the solution of integral inclusion.

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
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