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.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

scholarly journals Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 754 ◽  
Author(s):  
Reny George ◽  
Hossam A Nabwey ◽  
Rajagopalan Ramaswamy ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Admissible Pair ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Generalized Contraction ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.

scholarly journals Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1212
Author(s):  
Mathuraiveeran Jeyaraman ◽  
Mookiah Suganthi ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results.

scholarly journals Higher Order of Convergence with Multivalued Contraction Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jia-Bao Liu ◽  
Asma Rashid Butt ◽  
Shahzad Nadeem ◽  
Shahbaz Ali ◽  
Muhammad Shoaib
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Order Of Convergence ◽  
Higher Order ◽  
Gauge Function ◽  
Multivalued Mappings ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
Integral Inclusion

In this paper, we establish some theorems of fixed point on multivalued mappings satisfying contraction mapping by using gauge function. Furthermore, we use Q - and R -order of convergence. Our main results extend many previous existing results in the literature. Consequently, to substantiate the validity of proposed method, we give its application in integral inclusion.

scholarly journals Fixed Point Theorems for Ćirić-Berinde Type Contractive Multivalued Mappings

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Seong-Hoon Cho
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Multivalued Mappings ◽  
Contractive Condition

We give a Ćirić-Berinde type contractive condition for multivalued mappings and analyze the existence of fixed point for these mappings.

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