scholarly journals Common fixed points of (α-ψ)- generalized rational multivalued contractions in dislocated quasi b-metric spaces and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3263-3284 ◽  
Author(s):  
Mujahid Abbas ◽  
Vladimir Rakocevic ◽  
Bahru Leyew
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Continuous Solution ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Multivalued Operator ◽  
Multivalued Contractions ◽  
Rational Contraction

In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.

scholarly journals Common Fixed Point Results for a Pair of Multivalued Mappings in Complex-Valued b-Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Olawale Kazeem Oyewole ◽  
Kazeem Olalekan Aremu ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Liouville Equation ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Contractive Mappings ◽  
Complex Valued Metric Space ◽  
Complex Valued

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valued b-metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation.

scholarly journals Fixed points of asymptotically regular multivalued mappings

1992 ◽  
Vol 53 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Ismat Beg ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Coincidence Points ◽  
Asymptotically Regular

AbstractSome results on fixed point of asymptotically regular multivalued mapping are obtained in metric spaces. The structure of common fixed points and coincidence points of a pair of compatible multivalued mappings is also discussed. Our work generalizes known results of Aubin and Siegel, Dube, Dube and Singh, Hardy and Rogers, Hu, Iseki, Jungck, Kaneko, Nadler, Ray and Shiau, Tan and Wong.

scholarly journals Fixed points of multivalued contractions via generalized class of simulation functions

2019 ◽  
Vol 38 (3) ◽  
pp. 161-176
Author(s):  
Deepesh Kumar Patel
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Simulation Functions ◽  
Multivalued Contractions

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in α-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well known fixed point results of the literature. Some examples and consequence are given to  illustrate the usability of the theory.

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 A New Class of Contraction inb-Metric Spaces and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Preeti Kaushik ◽  
Sanjay Kumar ◽  
Kenan Tas
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
New Class ◽  
End Results

A novel class ofα-β-contraction for a pair of mappings is introduced in the setting ofb-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals Common Fixed Points for Nonlinear Quasi-Contractions of Ćirić Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Positive Answer ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Scalarization Method ◽  
Cone Metric

We establish common fixed points theorems for two self-mappings satisfying a nonlinear contractive condition of Ćirić type with aQ-function. Furthermore, using the scalarization method, we deduce some results of common fixed point in tvs-cone metric spaces with ac-distance. As application, we give a positive answer to the question of Ćirić et al. posed in 2012. Our results extend and generalize many recent results.

scholarly journals Some new types multivalued F-contractions on quasi metric spaces and their fixed points

2019 ◽  
Vol 35 (1) ◽  
pp. 41-50
Author(s):  
HATICE ASLAN HANCER ◽  
◽  
MURAT OLGUN ◽  
ISHAK ALTUN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Fixed Point Result ◽  
Q Function

In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued Fd-contraction on quasi metric space (X, d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space.

scholarly journals Some common fixed points of multivalued mappings on complex-valued metric spaces with homotopy result

2017 ◽  
Vol 10 (07) ◽  
pp. 3381-3396 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Mohd Salmi MD Norani ◽  
Jamshaid Ahmad ◽  
Habes Alsamir ◽  
Marwan Amin Kutbi
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Homotopy Result ◽  
Complex Valued
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