Research Article
BibTex RIS Cite

Year 2018, , 85 - 87, 30.06.2018

Erdal Karapinar

https://doi.org/10.31197/atnaa.431135
Cited By: 92

Abstract

References

  • [1] R. Kannan, Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76 (1968).
  • [2] R. Kannan, Some results on fixed points. II. Am. Math. Mon. 76, 405-408 (1969.

Revisiting the Kannan Type Contractions via Interpolation

Year 2018, , 85 - 87, 30.06.2018

Erdal Karapinar

https://doi.org/10.31197/atnaa.431135
Cited By: 92

Abstract

In the paper, we revisited the well-known fixed point theorem of Kannan under the aspect of interpolation. By using the interpolation notion, we propose a new Kannan type contraction  to maximize the rate of convergence.

Keywords

Kannan Type Contraction Interpolation fixed point rate of convergence

References

  • [1] R. Kannan, Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76 (1968).
  • [2] R. Kannan, Some results on fixed points. II. Am. Math. Mon. 76, 405-408 (1969.
There are 2 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Erdal Karapinar

Publication Date June 30, 2018
Published in Issue Year 2018

Cite

Cited By

Existence of fixed points of large MR-Kannan contractions in Banach Spaces
Applied General Topology
https://doi.org/10.4995/agt.2024.20852
Existence theorems for a unified interpolative Kannan contraction with an application on nonlinear matrix equations
Vojnotehnicki glasnik
https://doi.org/10.5937/vojtehg72-50753
On the relation of Kannan contraction and Banach contraction
Mathematica Slovaca
https://doi.org/10.1515/ms-2024-0094
ON FIXED POINTS OF INTERPOLATIVE CONVEX AND ALMOST CONVEX-TYPE CONTRACTIVE MAPPINGS
Journal of Science and Arts
https://doi.org/10.46939/J.Sci.Arts-24.1-a04
Rational interpolative contractions with applications in extended $ b $-metric spaces
AIMS Mathematics
https://doi.org/10.3934/math.2024683
On interpolative Hardy-Rogers type cyclic contractions
Applied General Topology
https://doi.org/10.4995/agt.2024.19885
Approximation and existence of fixed points via interpolative enriched contractions
Filomat
https://doi.org/10.2298/FIL2316455R
On a common fixed point theorem in vector-valued $ b $-metric spaces: Its consequences and application
AIMS Mathematics
https://doi.org/10.3934/math.20231326
Fixed points results for various types of interpolative cyclic contraction
Applied General Topology
https://doi.org/10.4995/agt.2023.19515
On interpolative R-Meir-Keeler contractions of rational forms
Filomat
https://doi.org/10.2298/FIL2309879O
Generalized common best proximity point results in fuzzy multiplicative metric spaces
AIMS Mathematics
https://doi.org/10.3934/math.20231299
SOLUTION OF FRACTIONAL INTEGRAL EQUATION VIA HYBRID CONTRACTIONS IN METRIC-LIKE SPACES
Poincare Journal of Analysis and Applications
https://doi.org/10.46753/pjaa.2023.v010i01.012
Interpolative Contractive Results for $m$-Metric Spaces
Advances in the Theory of Nonlinear Analysis and its Application
https://doi.org/10.31197/atnaa.1220114
On the Perov's type $ (\beta, F) $-contraction principle and an application to delay integro-differential problem
AIMS Mathematics
https://doi.org/10.3934/math.20231217
Fixed point theorems for interpolative $${\grave{\rm C}}{\text{iri}}{\grave{\rm c}}$$-type contraction mappings in convex hull combination of Busemann space with an application to fractional differential equations
The Journal of Analysis
https://doi.org/10.1007/s41478-023-00634-y
Fixed point theorems for relation-theoretic F-interpolative in branciari distance with an application
Physics & Astronomy International Journal
https://doi.org/10.15406/paij.2023.07.00296
Some fixed point results in rectangular metric spaces
Annals of Mathematics and Physics
https://doi.org/10.17352/amp.000089
ON WEAK INTERPOLATIVE CONTRACTIONS WITH APPLICATION TO HOMOTOPY THEORY
Journal of Science and Arts
https://doi.org/10.46939/J.Sci.Arts-23.2-a09
The (ψ,φ)-orthogonal interpolative contractions and an application to fractional differential equations
Filomat
https://doi.org/10.2298/FIL2304167N
Fixed point theorems for interpolative Ćirić-type contraction mappings in CAT (0) space with application to hyperbolical rotation matrix
The Journal of Analysis
https://doi.org/10.1007/s41478-023-00606-2
Kannan Type Contraction via Interpolation in Bipolar Metric Spaces
International Journal of Advanced Research in Science, Communication and Technology
https://doi.org/10.48175/IJARSCT-9677
Fixed point theorem on an orthogonal extended interpolative $ \psi\mathcal{F} $-contraction
AIMS Mathematics
https://doi.org/10.3934/math.2023825
On interpolative fuzzy contractions with applications
Filomat
https://doi.org/10.2298/FIL2301207M
A Study on Some Multi-Valued Interpolative Contractions
Communications in Advanced Mathematical Sciences
https://doi.org/10.33434/cams.794172
Fixed-Point Theorems for ω − ψ -Interpolative Hardy-Rogers-Suzuki-Type Contraction in a Compact Quasipartial b -Metric Space
Journal of Function Spaces
https://doi.org/10.1155/2023/3911534
Interpolative $KMK$-Type Fixed-Figure Results
Mathematical Sciences and Applications E-Notes
https://doi.org/10.36753/mathenot.1141344
On Some Novel Fixed Point Results for Generalized -Contractions in�Metric-Like Spaces with Application
Computer Modeling in Engineering & Sciences
https://doi.org/10.32604/cmes.2022.022878
On interpolative Hardy-Rogers type multivalued contractions via a simulation function
Filomat
https://doi.org/10.2298/FIL2208847K
Fixed point results of enriched interpolative Kannan type operators with applications
Applied General Topology
https://doi.org/10.4995/agt.2022.16701
Fixed point Theorem for Interpolative Mappings in F-Mv -Metric Space with an Application
Topological Algebra and its Applications
https://doi.org/10.1515/taa-2022-0120
A new approach to generalized interpolative proximal contractions in non archimedean fuzzy metric spaces
AIMS Mathematics
https://doi.org/10.3934/math.2023151
New techniques on fixed point theorems for symmetric contraction mappings with its application
AIMS Mathematics
https://doi.org/10.3934/math.2023457
Remarks on the generalized interpolative contractions and some fixed-point theorems with application
Open Mathematics
https://doi.org/10.1515/math-2022-0042
Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique
Symmetry
https://doi.org/10.3390/sym14081504
$ \acute{C} $iri$ \acute{c} $-Reich-Rus type weakly contractive mappings and related fixed point results in modular-like spaces with application
AIMS Mathematics
https://doi.org/10.3934/math.2022898
Best Proximity Point Theorems for the Generalized Fuzzy Interpolative Proximal Contractions
Fractal and Fractional
https://doi.org/10.3390/fractalfract6080455
Fixed point results for interpolative $$\psi$$-Hardy-Rogers type contraction mappings in quasi-partial b-metric space with an applications
The Journal of Analysis
https://doi.org/10.1007/s41478-022-00456-4
Fixed points of interpolative Matkowski type contraction and its application in solving non-linear matrix equations
Rendiconti del Circolo Matematico di Palermo Series 2
https://doi.org/10.1007/s12215-022-00789-w
Fixed point theorems for interpolative Kanann contraction mappings in Busemann space with an application to matrix equation
The Journal of Analysis
https://doi.org/10.1007/s41478-022-00502-1
On Interpolative Prešić-Type Set-Valued Contractions
Journal of Mathematics
https://doi.org/10.1155/2022/4194875
Fixed Points of Proinov Type Multivalued Mappings on Quasimetric Spaces
Journal of Function Spaces
https://doi.org/10.1155/2022/7197541
A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces
Mathematics
https://doi.org/10.3390/math9233001
Interpolative Prešić Type Contractions and Related Results
Journal of Function Spaces
https://doi.org/10.1155/2022/6911475
New Fixed Point Theorems for Admissible Hybrid Maps
Journal of Function Spaces
https://doi.org/10.1155/2022/5800790
Some New Results for a Class of Multivalued Interpolative Kannan-Type Contractions
Axioms
https://doi.org/10.3390/axioms11020076
On some results on interpolative Kannan-type and CRR-type contractions.
Moroccan Journal of Pure and Applied Analysis
https://doi.org/10.2478/mjpaa-2022-0005
Discussion on the hybrid Jaggi-Meir-Keeler type contractions
AIMS Mathematics
https://doi.org/10.3934/math.2022703
Interpolative Ćirić-Reich-Rus-type best proximity point results with applications
AIMS Mathematics
https://doi.org/10.3934/math.2022542
On Nonunique Fixed Point Theorems via Interpolative Chatterjea Type Suzuki Contraction in Quasi-Partial b-Metric Space
Journal of Mathematics
https://doi.org/10.1155/2022/2347294
Interpolative contractions and intuitionistic fuzzy set-valued maps with applications
AIMS Mathematics
https://doi.org/10.3934/math.2022600
Revisiting Ciric type nonunique fixed point theorems via interpolation
Applied General Topology
https://doi.org/10.4995/agt.2021.16562
Fixed point index computations for multivalued mapping and application to the problem of positive eigenvalues in ordered space
Applied General Topology
https://doi.org/10.4995/agt.2022.15669
Generalized Interpolative Contractions and an Application
Journal of Mathematics
https://doi.org/10.1155/2021/6461477
θ*-Weak Contractions and Discontinuity at the Fixed Point with Applications to Matrix and Integral Equations
Axioms
Atiya Perveen
https://doi.org/10.3390/axioms10030209
Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions
Analele Universitatii "Ovidius" Constanta - Seria Matematica
Erdal Karapınar
https://doi.org/10.2478/auom-2019-0038
On p-Hybrid Wardowski Contractions
Journal of Mathematics
Erdal Karapınar
https://doi.org/10.1155/2020/1632526
(ρ,η,μ)-Interpolative Kannan Contractions I
Axioms
Yaé Ulrich Gaba
https://doi.org/10.3390/axioms10030212
From interpolative contractive mappings to generalized Ciric-quasi contraction mappings
Applied General Topology
Kushal Roy
https://doi.org/10.4995/agt.2021.14045
New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces
Journal of Function Spaces
Muhammad Usman Ali
https://doi.org/10.1155/2021/6641342
Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces
Mathematics
Antonio Francisco Roldán López de Hierro
https://doi.org/10.3390/math9141594
Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications
Journal of Function Spaces
Lili Chen
https://doi.org/10.1155/2020/7963242
Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space
Symmetry
Pragati Gautam
https://doi.org/10.3390/sym13010032
New Results on Perov-Interpolative Contractions of Suzuki Type Mappings
Journal of Function Spaces
Erdal Karapınar
https://doi.org/10.1155/2021/9587604
On Some Interpolative Contractions of Suzuki Type Mappings
Journal of Function Spaces
Andreea Fulga
https://doi.org/10.1155/2021/6596096
Interpolative Caristi type contractive mapping in an extended b-metric space
The Journal of Analysis
Kushal Roy
https://doi.org/10.1007/s41478-021-00342-5
Interpolative Kannan Contractions in T 0 -Quasi-Metric Spaces
Journal of Mathematics
Yaé Ulrich Gaba
https://doi.org/10.1155/2021/6685638
On Hybrid Contractions in the Context of Quasi-Metric Spaces
Mathematics
Andreea Fulga
https://doi.org/10.3390/math8050675
Interpolative Reich–Rus–Ćirić and Hardy–Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results
Mathematics
Vishnu Narayan Mishra
https://doi.org/10.3390/math8091598
On interpolative Hardy-Rogers contractive of Suzuki type mappings
Topological Algebra and its Applications
Seher Sultan Yeşilkaya
https://doi.org/10.1515/taa-2020-0102
On admissible hybrid Geraghty contractions
Carpathian Journal of Mathematics
ERDAL KARAPINAR
https://doi.org/10.37193/CJM.2020.03.11
Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces
Symmetry
Pradip Debnath
https://doi.org/10.3390/sym12010012
An admissible Hybrid contraction with an Ulam type stability
Demonstratio Mathematica
Erdal Karapınar
https://doi.org/10.1515/dema-2019-0037
Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction
Journal of Mathematics
Youssef Errai
https://doi.org/10.1155/2021/9992783
Admissible Hybrid Z-Contractions in b-Metric Spaces
Axioms
Ioan Cristian Chifu
https://doi.org/10.3390/axioms9010002
Some Fixed Point Results of Kannan Maps on the Nakano Sequence Space
Journal of Function Spaces
Awad A. Bakery
https://doi.org/10.1155/2021/2578960
Interpolative Kannan- Meir-Keeler type contraction
Advances in the Theory of Nonlinear Analysis and its Application
Erdal KARAPINAR
https://doi.org/10.31197/atnaa.989389
Fixed points of nonlinear contractions with applications
AIMS Mathematics
Mohammed Shehu Shagari
https://doi.org/10.3934/math.2021545
A study of symmetric contractions with an application to generalized fractional differential equations
Advances in Difference Equations
Aftab Hussain
https://doi.org/10.1186/s13662-021-03456-z
Fixed-Point Theorems for Rational Interpolative-Type Operators with Applications
Journal of Function Spaces
Muhammad Sarwar
https://doi.org/10.1155/2020/7816505
Some theorems in partial metric space using auxiliary functions
AIMS Mathematics
Deepak Kumar
https://doi.org/10.3934/math.2021396
On Jaggi-Suzuki-Type Hybrid Contraction Mappings
Journal of Function Spaces
Maha Noorwali
https://doi.org/10.1155/2021/6721296
A New Approach to the Interpolative Contractions
Axioms
Yaé Ulrich Gaba
https://doi.org/10.3390/axioms8040110
Discussion on Geraghty Type Hybrid Contractions
Journal of Function Spaces
Sara Salem Alzaid
https://doi.org/10.1155/2020/6614291
Some Remarks on Fixed Point Theorems for Interpolative Kannan Contraction
Journal of Function Spaces
Youssef Errai
https://doi.org/10.1155/2020/2075920
Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces
Axioms
Youssef Errai
https://doi.org/10.3390/axioms9040132
Generalizations of Kannan and Reich Fixed Point Theorems, Using Sequentially Convergent Mappings and Subadditive Altering Distance Functions
Mathematics
Alireza Pourmoslemi
https://doi.org/10.3390/math8091432
On Interpolative Hardy-Rogers Type Contractions
Symmetry
Erdal Karapınar
https://doi.org/10.3390/sym11010008
Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces
Mathematics
Erdal Karapinar
https://doi.org/10.3390/math6110256
Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance
Mathematics
Hassen Aydi
https://doi.org/10.3390/math7010084
A Hybrid Contraction that Involves Jaggi Type
Symmetry
Erdal Karapınar
https://doi.org/10.3390/sym11050715
ω-Interpolative Ćirić-Reich-Rus-Type Contractions
Mathematics
Hassen Aydi
https://doi.org/10.3390/math7010057
New Hybrid Contractions on b-Metric Spaces
Mathematics
Karapinar
https://doi.org/10.3390/math7070578