scholarly journals Ciric type generalized F-contractions on completemetric spaces and fixed point results

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1143-1151 ◽  
Author(s):  
Gülhan Mınak ◽  
Asuman Helvacı ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Proper Generalization ◽  
Type Contraction

Recently, Wardowski [15] introduced the concept of F-contraction on complete metric space. This type contraction is proper generalization of ordinary contraction. In the present paper, we give some fixed point results for generalized F-contractions including Ciric type generalized F-contraction and almost F-contraction on complete metric space. Also, we give some illustrative examples.

scholarly journals Orbital continuity and fixed points

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3495-3499 ◽  
Author(s):  
Abhijit Pant ◽  
R.P. Pant
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Sufficient Condition ◽  
Point Property ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Type Contraction

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type Af or of type A1 of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

scholarly journals A discussion on a Pata type contraction via iterate at a point

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1061-1066
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga ◽  
Vladimir Rakocevic
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Continuity Assumption ◽  
The Given ◽  
Type Contraction

In this paper, we introduce the notion of Pata type contraction at a point in the context of a complete metric space. We observe that such contractions possesses unique fixed point without continuity assumption on the given mapping. Thus, is extended the original results of Pata. We also provide an example to illustrate its validity.

scholarly journals A New Approach to Common Coupled Fixed Point of Caristi Type Contraction on a Metric Space Endowed with a Graph

2018 ◽  
Vol 7 (4.10) ◽  
pp. 323
Author(s):  
G. Adilakshmi ◽  
G. N.V.Kishore ◽  
N. Konda Reddy
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Edge Preserving ◽  
New Approach ◽  
Common Coupled Fixed Point ◽  
Type Contraction

In this paper we introduced a new notation G – fg –   contraction of Caristi type and a new edge preserving property. With help of these we proved a some coupled fixed point results for four maps endowed with a graph in a complete metric space. Also we gave an application to integral equations. 

scholarly journals Interpolative Reich–Rus–Ćirić and Hardy–Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1598 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz ◽  
Pragati Gautam ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contraction Condition ◽  
Common Fixed Point Theorem ◽  
Type Contraction

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich–Rus–Ćirić type contraction and Hardy–Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

scholarly journals (ρ,η,μ)-Interpolative Kannan Contractions I

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 212
Author(s):  
Yaé Ulrich Gaba ◽  
Hassen Aydi ◽  
Nabil Mlaiki
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Equivalent Formulation ◽  
Kannan Contraction ◽  
Type Contraction

We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.

On Fixed Point Theorems in Complete Metric Space

2019 ◽  
Vol 10 (7) ◽  
pp. 1419-1425
Author(s):  
Jayashree Patil ◽  
Basel Hardan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space

scholarly journals Common Fixed Point for Generalized Bose-Mukherjee-Type Fuzzy Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Ming-liang Song ◽  
Zhong-qian Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Common Fixed Point Theorem

We prove a common fixed point theorem for a pair of generalized Bose-Mukherjee-type fuzzy mappings in a complete metric space. An example is also provided to support the main result presented herein.

scholarly journals Suzuki ψF-contractions and some fixed point results

2018 ◽  
Vol 34 (1) ◽  
pp. 93-102
Author(s):  
NICOLAE-ADRIAN SECELEAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuity Point ◽  
Picard Operator ◽  
Nonlinear Anal ◽  
New Type

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.

scholarly journals Fixed point and a Cantilever beam problem in a partial b-metric space

2021 ◽  
Vol 13 (2) ◽  
pp. 506-518
Author(s):  
Anita Tomar ◽  
Meena Joshi ◽  
Venkatesh Bhatt
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Cantilever Beam ◽  
Metric Space ◽  
Elastic Beam ◽  
The Common ◽  
Type Contraction

Abstract We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.

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