Set-valued contraction mappings of Prešić–Reich type in ultrametric spaces

2017 ◽  
Vol 10 (04) ◽  
pp. 1750065 ◽  
Author(s):  
D. Ramesh Kumar ◽  
M. Pitchaimani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Ultrametric Spaces ◽  
Contraction Mappings

In this paper, we introduce the concept of set-valued Prešić–Reich type contractive condition in ultrametric spaces and establish the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping besides furnishing illustrative examples to highlight the realized improvements in the context of ultrametric spaces. Our results generalize and extend some known results in the literature.

scholarly journals Fixed points of relaxed (Ψ,φ)-weakly N-contraction mappings in modular spaces

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1659-1676
Author(s):  
Getahun Wega ◽  
Habtu Zegeye ◽  
Oganeditse Boikanyo
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Contraction Mapping ◽  
Contractive Condition ◽  
Numerical Examples ◽  
Contraction Mappings ◽  
Modular Spaces

The purpose of this paper is to study the existence and approximation of a common fixed point of a pair of mappings satisfying a relaxed (?,?)-weakly N-contractive condition and existence and approximation of a fixed point of a relaxed (?,?)-weakly N-contraction mapping in the setting of modular spaces. Our theorems improve and generalize the results in Mongkolkeha and Kumam [23] and ?zt?rk et. al [26]. To validate our results numerical examples are provided.

A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces

2020 ◽  
Vol 70 (6) ◽  
pp. 1367-1380
Author(s):  
Rale M. Nikolić ◽  
Vladimir T. Ristić ◽  
Nataša A. Ćirović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Strictly Convex ◽  
Common Fixed Point Theorem ◽  
Commuting Mappings

AbstractIn this paper we prove existence and uniqueness of a common fixed point for non-self coincidentally commuting mappings with nonlinear, generalized contractive condition defined on strictly convex Menger PM-spaces proved.

On Nadler type results in ultrametric spaces with application to well-posedness

2017 ◽  
Vol 10 (04) ◽  
pp. 1750073 ◽  
Author(s):  
M. Pitchaimani ◽  
D. Ramesh Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Ultrametric Spaces ◽  
Common Fixed Point Problem ◽  
Set Valued Mappings

In this paper, we generalize Nadler’s result by establishing the existence and uniqueness of coincidence and common fixed points of Nadler’s type set-valued mappings in ultrametric spaces. Examples are given to illustrate the results. As an application, well-posedness of a common fixed point problem is proved. The presented results generalize many known results in literature in the framework of ultrametric spaces.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

scholarly journals Common fixed point theorem for four mappings satisfying generalized weak contractive condition

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 1-10 ◽  
Author(s):  
Mujahid Abbas ◽  
Dragan Djoric
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Applied Mathematics ◽  
Point Theory ◽  
Contractive Condition ◽  
Mathematics Subject Classifications ◽  
Common Fixed Point Theorem

Contractive conditions introduced in (Q. Zhang and Y. Song, Fixed point theory for generalized ?-weak contraction, Appl. Math. Lett. 22(2009), 75-78) and (D. Djoric, Common fixed point for generalized (?, ?)-weak contractions, Applied Mathematics Letters, 22(2009), 1896-1900) are employed to obtain a new common fixed point theorem for four maps. Our result substantially generalizes comparable results in the literature. 2010 Mathematics Subject Classifications. 47H10. .

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