Common fixed point theorems of Meir-Keeler contraction type in complex valued metric space and an application to dynamic programming

2021 ◽  
pp. 1-17
Author(s):  
Khaled Berrah ◽  
Taki eddine Oussaeif ◽  
Abdelkrim Aliouche
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complex Valued Metric Space ◽  
Contraction Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

scholarly journals Common Fixed Point Results for Six Mappings via Integral Contractions with Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Mian Bahadur Zada ◽  
Muhammad Sarwar ◽  
Nayyar Mehmood
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type Inequality ◽  
Dynamical Programming ◽  
System Of Functional Equations ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Common fixed point theorems for six self-mappings under integral type inequality satisfying (E.A) and (CLR) properties in the context of complex valued metric space (not necessarily complete) are established. The derived results are new even for ordinary metric spaces. We prove existence result for optimal unique solution of the system of functional equations used in dynamical programming with complex domain.

scholarly journals Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 74 ◽  
Author(s):  
Haitham Qawaqneh ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Type Mapping ◽  
Admissible Mapping ◽  
Contraction Type ◽  
Common Fixed Point Theorems

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.

Two Generalized Common Fixed Point Theorems Involving Compatibility and Property E.A.

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
T. Phaneendra ◽  
V. S. R. Prasad
Keyword(s):  
Fixed Point ◽  
Recent Result ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Type Inequality ◽  
Compatible Maps ◽  
Significant Generalization ◽  
Contraction Type ◽  
Common Fixed Point Theorems

AbstractWe prove two generalizations: the first to Das and Naik’s theorem for a pair of compatible maps without continuity; and the next as an extension of our first result to three self-maps on a metric space X without compatibility, under a stronger contraction type inequality and restricting the completeness of X to its subspace. The latter is a significant generalization of a recent result of Pant et al.

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 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 FIXED POINT THEOREMS USING (CLCS) PROPERTY IN COMPLEX VALUED $b$-METRIC SPACES

2017 ◽  
pp. 269
Author(s):  
Rohit Kumar Verma
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Mappings ◽  
Common Limit ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Abstract. Various common fixed point theorems have been proved for oneor two pair of mappings using either (CLR) property ([24]), or by takingone of the range-subspace closed. In this paper, we introduce the notion of(CLCS)-property i.e., “common limit converging in the range sub-space”. Using this property, we prove common fixed point theorems for two pairs ofweakly compatible mappings in complex valued b-metric spaces satisfying acollection of contractive conditions. Our notion is meaningful and valid because the required common fixed point will always lie on the range-subspace of the mapping-pair. We give some examples to show that if a mapping pair (f, g) of a closed complex valued b-metric space X satisfy the (CLRf ) property, then it is also (CLRg), and vice-versa.

scholarly journals Reich, Jungck, and Berinde Common Fixed Point Results on ℱ-Metric Spaces and an Application

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 387 ◽  
Author(s):  
Zoran D. Mitrović ◽  
Hassen Aydi ◽  
Nawab Hussain ◽  
Aiman Mukheimer
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Point Theorems

Jleli and Samet (2018) introduced a new concept, named an F -metric space, as a generalization of the notion of a metric space. In this paper, we prove certain common fixed point theorems in F -metric spaces. As consequences of our results, we obtain results of Banach, Jungck, Reich, and Berinde in these spaces. An application in dynamic programming is also given.

scholarly journals Common fixed point theorems in complex valued non-negative extended b-metric space

2021 ◽  
Vol 2021 (1) ◽  
pp. 35-47
Author(s):  
Naimat Ullah ◽  
Mohammed Shehu Shagari ◽  
Tahir Ahmad Khan ◽  
Aziz Ullah Khan ◽  
Muhammad Atta Ullah Khan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Abstract We introduce complex valued non-negative extended b-metric spaces and establish new fixed point results for mappings under some rational contractions. Our idea improves and extends corresponding fixed point theorems in the setting of b-metric, extended b-metric and classical metric spaces. Nontrivial examples are provided to support the hypotheses and usefulness of the main result obtained herein.

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