Nonlinear Functional Analysis and Applications
Kyungnam University, Department of Mathematics Eduaction (BSRI)
- Quarterly
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- 1229-1595(pISSN)
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- 2466-0973(eISSN)
Volume 28 Issue 4
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This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.
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The first result of this paper is to give a revised proof of Sanatammappa et al.'s recent result in a b-metric space, under appropriate choice of constants without using the continuity of the b-metric. The second is to prove a fixed point theorem under a contraction type condition in an extended b-metric space.
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In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y2] + [x2, f(y)] on a 𝜌-complete convex modular *-algebra χ𝜌 by using ∆2-condition via convex modular 𝜌.
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This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.
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Rashmi Rekha Sahoo;N. Reingachan;Robinson Soraisam;Khangembam Babina Devi;Barchand Chanam 919
Let P(z) be a polynomial of degree n and P(z) ≠ 0 in |z| < 1. Then for every real α and R > 1, Aziz [1] proved that$$\max\limits_{{\mid}z{\mid}=1}{\mid}P(Rz)-P(z){\mid}{\leq}{\frac{R^n-1}{2}}(M^2_{\alpha}+M^2_{{\alpha}+{\pi}})^{\frac{1}{2}}{\mid},$$ where$$M{\alpha}={\max\limits_{1{\leq}k{\leq}n}}{\mid}P(e^{i({\alpha}+2k{\pi})n}){\mid}.$$ In this paper, we establish some improvements and generalizations of the above inequality concerning the polynomials and their ordinary derivatives. -
Thiyam Thadoi Devi;Khundrakpam Binod Mangang;Lalhmangaihzuala 929
In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property. -
Istayan Das;Robinson Soraisam;Mayanglambam Singhajit Singh;Nirmal Kumar Singha;Barchand Chanam 943
Let p(z) be a polynomial of degree n and for any complex number 𝛽, let D𝛽p(z) = np(z) + (𝛽 - z)p'(z) denote the polar derivative of the polynomial with respect to 𝛽. In this paper, we consider the class of polynomial$$p(z)=(z-z_0)^s \left(a_0+\sum\limits_{{\nu}=0}^{n-s}a_{\nu}z^{\nu}\right)$$ of degree n having a zero of order s at z0, |z0| < 1 and the remaining n - s zeros are outside |z| < k, k ≥ 1 and establish upper bound estimates for the maximum of |D𝛽p(z)| as well as |p(Rz) - p(rz)|, R ≥ r ≥ 1 on the unit disk. -
We define new classes of expansive-type mappings in the setting of modular 𝜔G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔G-complete modular 𝜔G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.
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Awad T. Alabdala;Alan jalal abdulqader;Saleh S. Redhwan;Tariq A. Aljaaidi 989
In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings. -
In this paper, we establish the existence of at least two distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold.
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Iqbal Jebril;Yazid GOUARI;Mahdi RAKAH;Zoubir DAHMANI 1017
In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e1, e2, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows. -
Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z(𝜔)r)-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.
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Abubakar Adamu;Dilber Uzun Ozsahin;Abdulkarim Hassan Ibrahim;Pongsakorn Sunthrayuth 1051
In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established. -
Altaf A. Bhat;Faiza A. Sulaiman;Javid A. Ganie;M. Younus Bhat;D. K. Jain 1069
The natural transform is represented by two (p, q)-analogues, and their comparative characteristics are established. To resolve some (p, q)-difference and functional equations, applications are carried out. -
In this paper, the concept of a weighted bν(α)-metric space is introduced as a generalization of the bν(s)-metric space and ν-metric space. We prove some fixed point results of the Reich-type contraction in the weighted bν(α)-metric space. Furthermore, we generalize Reich's theorem by extending the result to a weighted bν(α)-metric space.
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Chatuphol Khaofong;Phachara Saipara;Anantachai Padcharoen 1097
In this paper, we extend some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Hardy-Roger type mappings. Our result generalizes many known results in fixed point theory. Finally, we offer a example to illustrate our result. -
This paper deals with the controllability of linear and nonlinear generalized fractional dynamical systems in finite dimensional spaces. The results are obtained by using fractional calculus, Mittag-Leffler function and Schauder's fixed point theorem. Observability of linear system is also discussed. Examples are given to illustrate the theory.
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The purpose of this paper, we prove convergence theorems of the modified viscosity inexact Mann iteration process for a family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. We also show that the limit of the modified viscosity inexact Mann iteration {xn} solves the solution of some variational inequality.