Communications in Nonlinear Analysis
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Communications in Nonlinear Analysisendaily1Sat, 01 Oct 2022 00:00:00 +0330Sat, 01 Oct 2022 00:00:00 +0330ALGORITHM FOR EQUATIONS OF HAMMERSTEIN TYPE AND APPLICATIONS
https://www.cna-journal.com/article_139947.html
Equations of Hammerstein type cover large variety of areas and are of much interest to a wide audience due to the fact that they have applications in numerous areas. Suitable conditions are imposed to obtain a strong convergence result for nonlinear integral equations of Hammerstein type with monotone type mappings. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear has been used in this study to obtain the strong convergence result. Moreover, our technique is applied to show the forced oscillations of finite amplitude of a pendulum as a specific example of nonlinear integral equations of Hammerstein type. Numerical example is given for the illustration of the convergence of the sequences of iteration. These are done to demonstrate to our readers that this approach can be applied to problems arising in physical systems.Fixed points of Nesic type contraction maps in Convex metric spaces
https://www.cna-journal.com/article_145282.html
We define Nesic type contraction maps in convex metric spaces and prove the existence and uniqueness of fixed points of these maps in convex metric spaces. Our results extend the results of Nesic ([1], Results on fixed points of asymptotically regular mappings ) from the metric space setting to convex metricspaces.Measures of Noncompactness on Ω-distance Spaces.
https://www.cna-journal.com/article_148814.html
. The aim of this article is to present a new framework for studying measures of noncompactness in G-metric spaces. First, we introduce the concept of Ω-distance space as an Ω-measure of non-compactness on G-metric spaces. Finally, we use our main result to characterize G-metric completeness.SOME LP− TYPE INEQUALITIES FOR POLAR DERIVATIVE OF A POLYNOMIAL
https://www.cna-journal.com/article_151641.html
In this paper, we shall prove some Lpinequalities for the polar derivative of a polynomial having zerosin |z| &le; k &le; 1 and thereby obtain generalizations and refinements of an integral inequality due to Barchand Charamet alStrong convergence of monotone hybrid algorithms for maximal monotone mappings and generalized nonexpansive mappings
https://www.cna-journal.com/article_155362.html
A class of generalized nonexpansive mappings in Banach spaces is considered and a new monotone hybrid algorithm is presented for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping. Under certain conditions on the associated parameters, a strong convergence result is established. Moreover, the obtained result is applied to prove a strong convergence theorem for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping in a Hilbert space.A monotone hybrid algorithm for maximal monotone operators and a family of generalized nonexpansive mappings
https://www.cna-journal.com/article_160209.html
In this paper, a new monotone hybrid method is introduced in the framework of Banach spaces for finding a common element of the set of zeros of a maximum monotone operator and the fixed point set of a family of generalized nonexpansive mappings. The prove is given in the framework of Banach spaces for the strong convergence of a sequence of iteration to a common element of the set of zeros of a maximum monotone operator and the fixed point set of a family of generalized nonexpansive mappings. New convergence results are obtained for resolvents of maximal monotone operators and a family of generalized nonexpansive mappings in a Banach space.Monotone Method for System of Riemann-Liouville Fractional Differential Equations with Deviating Arguments under Integral Boundary Conditions
https://www.cna-journal.com/article_160210.html
Abstract
The aim of this paper is to develop a monotone iterative technique by intro-
ducing upper and lower solutions to Riemann-Liouville fractional differential
equations with deviating arguments and integral boundary conditions. As an
application of this technique ,existence and uniqueness results are obtained.THE SOLUTIONS OF SYSTEMS OF RATIONAL DIFFERENCE EQUATIONS IN TERMS OF FIBONACCI NUMBERS
https://www.cna-journal.com/article_166219.html
In this paper, we get the form of the solutions of the following difference equation systems with nonzero real numbers initial conditions
z(n+1) =w(n)(z(n-4) + w(n-5))/w(n-5) + z(n-4) - w(n),
w(n+1) =z(n-3)(z(n-3) + w(n-4)/2z(n-3) + w(n-4).
z(n+1) =w(n)(w(n-5) -z(n-4))/w(n-5)- z(n-4) + w(n),
w(n+1) =z(n-3)(w(n-4) -z(n-3)/w(n-4)Existence and stability for Ambartsumian equation with -Hilfer generalized proportional fractional derivative
https://www.cna-journal.com/article_171340.html
The main objective of this paper is to study the Ambartsumian equation in the sense of Hilfer Generalized proportional fractional derivative(HGPFD). The existence and stability properties of solution are studied. The technique used for study is fixed point theorem and Gronwall inequality. Ulam-Hyers-Rassias stability of the solution is also investigated.