scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

scholarly journals Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Imo Kalu Agwu ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Approximation Algorithms ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Type Condition ◽  
Iterative Schemes ◽  
Convergence And Stability ◽  
Contractive Type ◽  
Stability Results

We present new fixed points algorithms called multistep H-iterative scheme and multistep SH-iterative scheme. Under certain contractive-type condition, convergence and stability results were established without any imposition of the ’sum conditions’, which to a large extent make some existing iterative schemes so far studied by other authors in this direction practically inefficient. Our results complement and improve some recent results in literature.

scholarly journals Approximate Solution of Systems of Volterra Integral Equations of Second Kind by Adomian Decomposition Method

2015 ◽  
Vol 63 (1) ◽  
pp. 15-18
Author(s):  
Md Shariful Islam ◽  
Mir Shariful Islam ◽  
Md Zavid Iqbal Bangalee ◽  
AFM Khodadad Khan ◽  
Amal Halder
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Integral Equations ◽  
Decomposition Method ◽  
Real Life ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Life Problems ◽  
Adomian Decomposition ◽  
Differential And Integral Equations

Real life problems that arise in different branches of science and social science, in the form of differential and integral equations are non-linear in nature. However, methods developed in Mathematics, usually, are suitable for the linear system. In this article, we talk on approximating solution of system of Volterra integral equations of second kind in an analytic way using Adomian decomposition method in Mathematica. DOI: http://dx.doi.org/10.3329/dujs.v63i1.21761 Dhaka Univ. J. Sci. 63(1): 15-18, 2015 (January)

scholarly journals Fixed points of a finite family of I-asymptotically quasi-nonexpansive mappings in a convex metric space

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2175-2182 ◽  
Author(s):  
Birol Gündüz
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Error Terms

In this paper, we study Ishikawa iterative scheme with error terms for a finite family of Iasymptotically quasi-nonexpansive mappings in a convex metric space. We established strong convergence theorems and their applications for the proposed algorithms in a convex metric space. Our theorems improve and extend the corresponding known results in Banach spaces.

scholarly journals A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 271 ◽  
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Mathematical Modeling ◽  
Banach Space ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Real Life ◽  
System Of Nonlinear Equations ◽  
Life Problems ◽  
Lipschitz Constants ◽  
Better Than

Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu’s, Fisher’s, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes.

scholarly journals On Angrisani and Clavelli Synthetic Approaches to Problems of Fixed Points in Convex Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ljiljana Gajić ◽  
Mila Stojaković ◽  
Biljana Carić
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Continuity Condition ◽  
Fixed Point Problems ◽  
Convex Metric Space ◽  
Synthetic Approaches

The purpose of this paper is to prove some fixed point results for mapping without continuity condition on Takahashi convex metric space as an application of synthetic approaches to fixed point problems of Angrisani and Clavelli. Our results are generalizations in Banach space of fixed point results proved by Kirk and Saliga, 2000; Ahmed and Zeyada, 2010.

scholarly journals Existence of common fixed points via modified mann iteration in convex metric spaces and an invariant approximation result

2010 ◽  
Vol 41 (4) ◽  
pp. 335-348
Author(s):  
G.V.R. Babu ◽  
G.N. Alemayehu
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Space ◽  
Approximation Result ◽  
Mann Iteration ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Weakly Contractive

We prove the existence of common fixed points for two selfmaps $T$ and $f$ of a convex metric space $X$ via the convergence of modified Mann iteration where $T$ is a nonlinear $f$-weakly contractive selfmap of $X$ and range of $f$ is complete. An invariant approximation result is also proved.

scholarly journals Fixed points of non-self almost contractions

2014 ◽  
Vol 30 (1) ◽  
pp. 7-14
Author(s):  
MARYAM A. ALGHAMDI ◽  
◽  
VASILE BERINDE ◽  
NASEER SHAHZAD ◽  
◽  
...  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Space ◽  
Closed Subset ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Convex Metric Space

Let X be a convex metric space, K a non-empty closed subset of X and T : K → X a non-self almost contraction. Berinde and Pacurar [Berinde, V. and P ˘ acurar, M., Fixed point theorems for nonself single-valued almost contractions, Fixed Point Theory, 14 (2013), No. 2, 301–312], proved that if T has the so called property (M) and satisfies Rothe’s boundary condition, i.e., maps ∂K (the boundary of K) into K, then T has a fixed point in K. In this paper we observe that property (M) can be removed and, hence, the above fixed point theorem takes place in a different setting.

scholarly journals PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1375 ◽  
Author(s):  
Mohammed M. M. Jaradat ◽  
Babak Mohammadi ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Zead Mustafa
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
Control Engineering ◽  
Life Problems ◽  
Ulam Theorem ◽  
Delay Differential ◽  
And Control

The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of f ( x ) = x . One of such examples is that of the famous Borsuk–Ulam theorem, in which using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this paper, we initiate ϕ − F -contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.

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