scholarly journals Common fixed point theorems for expansive mappings via an implicit relation

2017 ◽  
Vol 2017 (1) ◽  
pp. 1-12
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Implicit Relation ◽  
Common Fixed Point Theorems

scholarly journals On compatible mappings satisfying an implicit relation in common fixed point consideration

2002 ◽  
Vol 33 (3) ◽  
pp. 245-252 ◽  
Author(s):  
Sushil Sharma ◽  
Bhavana Deshpande
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Implicit Relation ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed point theorems for compatible mappings satisfying an implicit relation.

scholarly journals Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

2019 ◽  
Vol 38 (4) ◽  
pp. 9-29
Author(s):  
Waleed Mohd Alfaqih ◽  
Mohammad Imdad ◽  
Fayyaz Rouzkard
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Implicit Relation ◽  
Common Solution ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

The purpose of this paper is to prove some common fixed point theorems for two pairs of weakly compatible mappings in complex valued metric spaces satisfying an implicit relation. Several illustrative examples are given which demonstrate the usefulness of our utilized implicit relation. Beside generalizing and improving several well known core results of the existing literature we can deduce several new contractions which have not obtained before in complex valued metric spaces. As an application of our results, we prove the existence and uniqueness of common solution of Hammerstein as well as Urysohn integral equations.

scholarly journals Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sunny Chauhan ◽  
Mohammad Imdad ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Compatible Mappings ◽  
Implicit Relation ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

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