scholarly journals Fixed and coupled fixed points of a new type set-valued contractive mappings in complete metric spaces

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
A Amini-Harandi
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
New Type ◽  
Coupled Fixed Points

scholarly journals Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Poom Kumam ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Partial Metric ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

scholarly journals On contractive mappings and discontinuity at fixed points

2020 ◽  
Vol 14 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Hiranmoy Garai ◽  
Lakshmi Dey ◽  
Yeol Cho
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Metric Spaces ◽  
Contractive Mappings ◽  
Interesting Open Problem

This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A`-contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

scholarly journals Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
W. Y. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Periodic Points ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

scholarly journals Fixed Points of Generalized (α, ψ, φ)-Rational Contractive Mappings in α-Complete Metric Spaces

2017 ◽  
Vol 59 (1) ◽  
pp. 13-28 ◽  
Author(s):  
G.V. Ravindranadh Babu ◽  
M. Dula Tolera
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings

AbstractIn this paper, we introduce generalized (α, ψ, φ)-rational contractive mappings in α-complete metric spaces and prove some new fixed point results for this class of mappings. We provide examples in support of our results. Our results generalize the fixed point results of Singh, Kamal, Sen and Chugh [22] and Piri and Kumam [18].

scholarly journals Unique Fixed Point Theorem for Weakly C-Contractive Mappings

1970 ◽  
Vol 5 (1) ◽  
pp. 6-13 ◽  
Author(s):  
Binayak S Choudhury
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Engineering And Technology ◽  
Existing Result

In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces. Key words: Metric space; Fixed point; Weak C-contraction. M S C (2000): 54H25   DOI: 10.3126/kuset.v5i1.2842 Kathmandu University Journal of Science, Engineering and Technology Vol.5, No.1, January 2009, pp 6-13

scholarly journals Fixed Points and Stability for Integral-Type Multivalued Contractive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhefu An ◽  
Mengyao Li ◽  
Liangshi Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Integral Type ◽  
Point Sets ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
The Stability ◽  
Fixed Point Sets

The existence and iterative approximations of fixed points concerning two classes of integral-type multivalued contractive mappings in complete metric spaces are proved, and the stability of fixed point sets relative to these multivalued contractive mappings is established. The results obtained in this article generalize and improve some known results in the literature. An illustrative example is given.

scholarly journals A variational principle, coupled fixed points and market equilibrium

2021 ◽  
Vol 26 (1) ◽  
pp. 169-185
Author(s):  
Stanimir Kabaivanov ◽  
Boyan Zlatanov
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Profit Maximization ◽  
Payoff Function ◽  
Response Functions ◽  
Barriers To Entry ◽  
Complete Metric Spaces ◽  
Oligopoly Markets ◽  
Coupled Fixed Points

We present a possible kind of generalization of the notion of ordered pairs of cyclic maps and coupled fixed points and its application in modelling of equilibrium in oligopoly markets. We have obtained sufficient conditions for the existence and uniqueness of coupled fixed in complete metric spaces. We illustrate one possible application of the results by building a pragmatic model on competition in oligopoly markets. To achieve this goal, we use an approach based on studying the response functions of each market participant, thus making it possible to address both Cournot and Bertrand industrial structures with unified formal method.We show that whenever the response functions of the two players are identical, then the equilibrium will be attained at equal levels of production and equal prices. The response functions approach makes it also possible to take into consideration different barriers to entry. By fitting to the response functions rather than the profit maximization of the payoff functions problem we alter the classical optimization problem to a problem of coupled fixed points, which has the benefit that considering corner optimum, corner equilibrium and convexity condition of the payoff function can be skipped.

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