scholarly journals Exciting Fixed Point Results on a Novel Space with Supportive Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hasanen A. Hammad ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Linear Equations ◽  
Topological Properties ◽  
Rlc Circuit ◽  
Complex Linear ◽  
New Space ◽  
Complex Valued ◽  
Theoretical Results

The goal of this paper is to present a new space, a complex valued controlled rectangular b -metric space (for short, υ ℂ -metric space). Some examples and topological properties of υ ℂ -metric spaces are given. Also, some related common fixed point results are discussed. Our results generalize a lot of works in this direction. Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. Finally, a numerical example to find the current that passes through the RLC circuit is illustrated.

scholarly journals Coincidence and Common Fixed Point Theorems via ϱ-Class Functions in Elliptic Valued Metric Spaces

2021 ◽  
Vol 29 (1) ◽  
pp. 165-182
Author(s):  
Mahpeyker Öztürk ◽  
Işıl A. Kösal ◽  
Hidayet H. Kösal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
New Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Abstract The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers 𝔼 p = { ∈ = υ + i ω : υ , ω ∈ ℝ ,     i 2 = p < 0 } , {\mathbb{E}_p} = \left\{ { \in = \upsilon + i\omega :\upsilon ,\omega \in \mathbb{R},\,\,{i^2} = p < 0} \right\}, and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.

scholarly journals Multivalued generalizations of fixed point results in fuzzy metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 211-22 ◽  
Author(s):  
Tatjana Došenovic ◽  
Dušan Rakic ◽  
Biljana Caric ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric ◽  
Altering Distance ◽  
Theoretical Results

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

scholarly journals Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jamshaid Ahmad ◽  
Chakkrid Klin-Eam ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Contractive Mappings ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011).

scholarly journals Complex Valued b-Metric Spaces and Common Fixed Point Theorems under Rational Contractions

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Anil Kumar Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Valued ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying certain rational contraction conditions in complex valued b-metric space. The obtained results generalize and extend some of the well-known results in the literature.

scholarly journals COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLEX VALUED b-METRIC SPACES

2017 ◽  
Vol 12 (12) ◽  
pp. 7014-7022
Author(s):  
Anil Kumar Dubey ◽  
Madhubala Kasar ◽  
Ravi Prakash Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we prove a common xed point theorem for weakly compatible mappings in complex valued b-metric space and also improve the condition of contraction of the results of M. Kumar et al.[7]. Further, we prove common xed point theorems for weakly compatible mappings with (E.A.) property and (CLRg) property.

scholarly journals Topological Structure of Quasi-Partial b-Metric Spaces

2016 ◽  
Vol 17 ◽  
pp. 8-18 ◽  
Author(s):  
Anuradha Gupta ◽  
Pragati Gautam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Topological Structure ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Topological Properties ◽  
Coupled Fixed Point Theorem ◽  
Metric Topology

In this paper we discuss the topological properties of quasi-partialb-metric spaces. The notion of quasi-partialb-metric space was introduced and fixed point theorem and coupled fixed point theorem on this space were studied. Here the concept of quasi-partialb-metric topology is discussed and notion of product of quasi-partialb-metric spaces is also introduced.

scholarly journals Common Fixed Point Results for Fuzzy Mappings on Complex-Valued Metric Spaces with Homotopy Results

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 61 ◽  
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Rational Expression ◽  
Complex Valued Metric Space ◽  
Homotopy Result ◽  
Complex Valued

Owing to the notion of a complex-valued metric space, we prove fixed point results, which generalize some common fixed point results under contractive condition for rational expression in the context of complex-valued metric spaces. In application, we present a homotopy result to apply the results obtained herein.

scholarly journals On Fuzzy Fixed-Point Results in Complex Valued Extended b-Metric Spaces with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Amnah Essa Shammaky ◽  
Jamshaid Ahmad ◽  
Abdelhamied Farrag Sayed
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Fuzzy Fixed Point ◽  
Complex Valued

The aim of this paper is to define fuzzy contraction in the context of complex valued extended b -metric space and prove fuzzy fixed-point results. Our results improve and extend certain recent results in literature. Moreover, we discuss an illustrative example to highlight the realized improvements. As application, we derive fixed-point results for multivalued mappings in the setting of complex valued extended b -metric space.

scholarly journals Common fixed point results in complex valued metric spaces with application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1363-1380 ◽  
Author(s):  
N. Hussain ◽  
Akbar Azam ◽  
Jamshaid Ahmad ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complex Valued Metric Space ◽  
Complex Valued

In this paper, common fixed point of six mappings satisfying a contractive condition involving rational inequality in the framework of complex valued metric space are obtained. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

scholarly journals A note on the paper "A fixed point theorems in Sb-metric spaces"

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3335-3346 ◽  
Author(s):  
Yumnam Rohen ◽  
Tatjana Dosenovic ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Common Fixed Point ◽  
Definition Of ◽  
Common Fixed Point Theorems ◽  
Theoretical Results

Very recently, N. Souayan and N. Mlaiki [Nazir Souayan and Nabil Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Comput. Sci. 16 (2016), 131-139] and S. Sedghi et al. [S. Sedghi, A. Gholidahneb, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixed point of four maps in Sb-metric spaces, to appear in J. Linear Topol. Algebra], introduced the concept of Sb-metric space as a generalization of S-metric space. In this paper, we modified the definition of Sb-metric introduced by Souayan and Mlaiki and prove some coupled common fixed point theorems in Sb-metric space. We also present an example to confirm our theoretical results.

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