scholarly journals A Generalization of Ćirić Quasicontractions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Erdal Karapınar ◽  
Kieu Phuong Chi ◽  
Tran Duc Thanh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Contractive Condition

We proved a fixed point theorem for a class of maps that satisfy Ćirić's contractive condition dependent on another function. We presented an example to show that our result is a real generalization.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

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. .

scholarly journals Two Fixed-Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type in the Modular Space

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam Beygmohammadi ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Contractive Condition ◽  
Integral Type

First we prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive inequality of integral type. Then we generalize fixed-point theorem for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974).

scholarly journals A New Common Fixed Point Theorem for Three Commuting Mappings

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 105
Author(s):  
Meryeme El Harrak ◽  
Ahmed Hajji
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Contractive Condition ◽  
Darbo’S Fixed Point Theorem ◽  
Common Fixed Point Theorem ◽  
Commuting Mappings

In the present paper, we propose a common fixed point theorem for three commuting mappings via a new contractive condition which generalizes fixed point theorems of Darbo, Hajji and Aghajani et al. An application is also given to illustrate our main result. Moreover, several consequences are derived, which are generalizations of Darbo’s fixed point theorem and a Hajji’s result.

scholarly journals A Common Fixed Point Theorem in Metric Space under General Contractive Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sunny Chauhan ◽  
Zoran Kadelburg ◽  
Sumitra Dalal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Contractive Condition ◽  
Continuous Mappings ◽  
Common Fixed Point Theorem

We prove a common fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings satisfying a general contractive condition in a metric space. Some illustrative examples are furnished to highlight the realized improvements. Our result improves the main result of Sedghi and Shobe (2007).

scholarly journals A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
J. Harjani ◽  
B. López ◽  
K. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type

The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of partially ordered metric spaces.

scholarly journals Fixed Point Theorems for Set-Valued Mappings under Contractive Condition in Quasi-Metric Spaces

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Mohseni Kolagar ◽  
Y.J. Cho ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Generalized Weak Contraction ◽  
Banach’S Fixed Point Theorem ◽  
Set Valued Mappings ◽  
Weakly Contractive

Abstract In this paper, we introduce the concept of a generalized weak contraction for set-valued mappings defined on quasi-metric spaces. We show the existence of fixed points for generalized weakly contractive set-valued mappings. Indeed, we have a generalization of Nadler’s fixed point theorem and Banach’s fixed point theorem in quasi-metric spaces and, further, investigate the convergence of iterate scheme of the form xn+1 ∈ Fxn with error estimates.

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