scholarly journals An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Rashad A. R. Bantan ◽  
Saif Ur Rehman ◽  
Shahid Mehmood ◽  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi ◽  
...  
Keyword(s):  
Metric Space ◽  
Fixed Point Theorems ◽  
Integral Operators ◽  
Integral Type ◽  
The One ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction ◽  
Unique Common Fixed Point

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

scholarly journals COMMON FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTION IN PARTIALLY ORDERED METRIC SPACE

2015 ◽  
Vol 11 (5) ◽  
pp. 5266-5275
Author(s):  
Gopi Prasad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Partially Ordered ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction

In this paper we prove some common fixed point theorems for two and four self-mappings using rational type contraction and some newly notified definitions in partially ordered metric space. In this way we generalized, modify, and extend some recent results due to Chandok and Dinu [14], Shantanwi and Postolache[28] and many others [1, 2, 4, 5, 21, 29, 30], thus generalizing results of Cabrea, Harjani and Sadarangani [12] as well as Dass and Gupta [15]  in the context of partial order metric setting.

scholarly journals Some Common Fixed Point Results for Rational Type Contraction Mappings in Complex Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Sumit Chandok ◽  
Deepak Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Weakly Compatible ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction

We prove some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces. The proved results generalize and extend some of the known results in the literature.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

scholarly journals Fixed Point Results on Multiplicative Semi-Metric Space

2020 ◽  
Vol 12 (3) ◽  
pp. 341-348
Author(s):  
B. Vijayabaskerreddy ◽  
V. Srinivas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems ◽  
Multiplicative Metric Space ◽  
Unique Common Fixed Point

  In this paper we introduce the notion of the Multiplicative Semi-Metric Space and proved common fixed point theorems. We establish fixed point theorems for four self-maps which can be extended to derive common fixed point theorems involving any finite number of mappings in Multiplicative Semi Metric Space. Further examples are discussed to show that compatible mappings of type-E, weakly compatible mappings and reciprocally-continuous mappings are weaker forms of compatible mappings and continuous mappings respectively. The main objective of this article is to prove the unique common fixed point theorems and employing the notion of the compatible mappings of type-E, reciprocally-continuous mappings in the Multiplicative Semi Metric Space. Our result generalizes the concept of Multiplicative Metric Space as it does not involve the multiplicative triangle inequality.

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.

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