scholarly journals Strong convergence of Picard and Mann iterations for strongly demicontractive multi-valued mappings

2020 ◽  
Vol 36 (2) ◽  
pp. 269-276
Author(s):  
PACHARA JAILOKA ◽  
◽  
VASILE BERINDE ◽  
SUTHEP SUANTAI ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Mann Iteration ◽  
New Class ◽  
Demicontractive Mappings ◽  
And Control ◽  
Conver Gence

A class of demicontractive mappings was first introduced in [Hicks, T. L. and Kubicek, J. D.,On the Mann ite-ration process in a Hilbert space, J. Math. Anal. Appl.,59(1977) 498–504 and M ̆arus ̧ter, S ̧ .,The solution by iterationof nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc.,63(1977), 69–73] and was first mentioned in thecase of multi-valued mappings in [Chidume, C. E., Bello, A. U. and Ndambomve, P.,Strong and∆-convergencetheorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT(0) spaces, Abstr.Appl. Anal.,2014(2014), https://doi.org/10.1155/2014/805168 and Isiogugu, F. O. and Osilike, M. O.,Conver-gence theorems for new classes of multivalued hemicontractive-type mappings, Fixed Point Theory Appl.,2014(2014),https://doi.org/10.1186/1687-1812-2014-93]. The demicontractivity with some weak smoothness conditionsensures only weak convergence of Mann iteration. In 2015, M ̆arus ̧ter and Rus [Kannan contractions and stronglydemicontractive mappings, Creat. Math. Inform.,24(2015), No. 2, 173–182], introduced a class of strongly de-micontractive mappings, and also discussed some relationships between strongly demicontractive mappingsand Kannan contractions. In this paper, we introduce a new class of strongly demicontractive multi-valuedmappings in Hilbert spaces. Strong convergence theorems of Picard and Mann iterative methods for stronglydemicontractive multi-valued mappings are established under some suitable coefficients and control sequences.

scholarly journals Stability for a New Class of GNOVI with (γG,λ)-Weak-GRD Mappings in Positive Hilbert Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Hong Gang Li ◽  
Yongqin Yang ◽  
Mao Ming Jin ◽  
Qinghua Zhang
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Variational Inclusions ◽  
New Class ◽  
Set Up ◽  
The Stability

By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions) with(γG,λ)-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained.

scholarly journals Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings

2015 ◽  
Vol 53 (1) ◽  
pp. 151-161
Author(s):  
Micah Okwuchukwu Osilike ◽  
Anthony Chibuike Onah
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iteration Scheme ◽  
Iteration Algorithm ◽  
Mann Iteration ◽  
Ishikawa Iteration ◽  
New Class ◽  
Hemicontractive Mappings ◽  
Demicontractive Mappings

Abstract A new class of α-hemicontractive maps T for which the strong convergence of the Ishikawa iteration algorithm to a fixed point of T is assured is introduced and studied. The study is a continuation of a recent study of a new class of α-demicontractive mappings T by L. Mărușter and Ș. Mărușter, Mathematical and Computer Modeling 54 (2011) 2486-2492 in which they proved strong convergence of the Mann iteration scheme to a fixed point of T. Our class of α-hemicontractive maps is more general than the class of α-demicontractive maps. No compactness assumption is imposed on the operator or it’s domain, and no additional requirement is imposed on the set of fixed points.

scholarly journals Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

2021 ◽  
Vol 7 (2) ◽  
pp. 2195-2219
Author(s):  
Muhammad Rafique ◽  
◽  
Talat Nazir ◽  
Mujahid Abbas ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Fuzzy Mathematics ◽  
New Class ◽  
Contractive Mappings ◽  
New Research

<abstract><p>We introduce a new class of generalized graphic fuzzy $ F $- contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.</p></abstract>

Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Hemant Nashine
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Partial Metric ◽  
New Class ◽  
Weakly Contractive Condition ◽  
Partial Metric Spaces ◽  
Weakly Contractive

AbstractIn [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

scholarly journals Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 59
Author(s):  
Ahmed Salem ◽  
Mohammad Alnegga
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of A Solution ◽  
New Class ◽  
Research Article ◽  
Analysis Technique ◽  
Modern Analysis

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

scholarly journals Approximations for Equilibrium Problems and Nonexpansive Semigroups

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Common Fixed Points ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Nonexpansive Semigroup ◽  
New Iterative Method

We introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of all common fixed points of a nonexpansive semigroup and prove the strong convergence theorem in Hilbert spaces. Our result extends the recent result of Zegeye and Shahzad (2013). In the last part of the paper, by the way, we point out that there is a slight flaw in the proof of the main result in Shehu's paper (2012) and perfect the proof.

scholarly journals Approximation of common fixed points of a finite family of Ø - demicontractive mappings by an implicit iteration method.

2015 ◽  
Vol 12 (1) ◽  
pp. 31-38
Author(s):  
DI Igbokwe ◽  
UE Udofia
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Finite Family ◽  
Implicit Iteration Process ◽  
Demicontractive Mappings ◽  
Implicit Iteration

We prove that the Implicit Iteration process of Xu and Ori (2001) converges strongly to the commonfixed pointsof a finite family of Ø - demicontractive mappings in real Hilbertand Banachspaces. Our results extend the results of Osilike (2004a) from strictl pseudocontractive maps to the much more general Ø - demicontractive maps;complement and generalize several others in the literature.KEY WORDS AND PHRASES: Ø - Demicontractive Maps, Implicit Iteration Process, Fixed Points,Strong Convergence.

scholarly journals Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5497-5509 ◽  
Author(s):  
Habes Alsamir ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Kamal Abodyah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Partial Metric ◽  
Partially Ordered ◽  
Partial Metric Spaces ◽  
Contraction Type

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

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