Nonlinear Functional Analysis and Applications
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
- 계간
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- 1229-1595(pISSN)
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- 2466-0973(eISSN)
제29권2호
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Nopparat Wairojjana;Nattawut Pholasa;Chainarong Khunpanuk;Nuttapol Pakkaranang 307
Two inertial extragradient-type algorithms are introduced for solving convex pseudomonotone variational inequalities with fixed point problems, where the associated mapping for the fixed point is a 𝜌-demicontractive mapping. The algorithm employs variable step sizes that are updated at each iteration, based on certain previous iterates. One notable advantage of these algorithms is their ability to operate without prior knowledge of Lipschitz-type constants and without necessitating any line search procedures. The iterative sequence constructed demonstrates strong convergence to the common solution of the variational inequality and fixed point problem under standard assumptions. In-depth numerical applications are conducted to illustrate theoretical findings and to compare the proposed algorithms with existing approaches. -
This paper is concerned with the radial solutions of a nonlinear elliptic equation ∆pu + |x|𝑙1 |u|q1-1 u + |x|𝑙2 |u|q2-1 u = 0, x ∈ ℝN, where p > 2, N ≥ 1, q2 > q1 ≥ 1, -p < 𝑙2 < 𝑙1 ≤ 0 and -N < 𝑙2 < 𝑙1 ≤ 0. We prove the existence of global solutions, we give their classification and we present the explicit behavior of positive solutions near the origin and infinity.
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In this paper, a pair of ω-compatible self mappings in the setting of modular G-metric space is defined. We prove the existence and uniqueness of common fixed point of pairs of ω-compatible self mappings in a G-complete modular G-metric space. Furthermore, we give an example to justify our claims. The results established in this paper extend, improve, generalize and complement some existing results in literature.
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In this paper, we propose a new inertial subgradient extragradient algorithm with a new linesearch technique that combines the inertial subgradient extragradient algorithm and the KrasnoselskiiMann algorithm. Under some suitable conditions, we prove a weak convergence theorem of the proposed algorithm for finding a common element of the common solution set of a finitely many variational inequality problem and the fixed point set of a nonexpansive mapping in real Hilbert spaces. Moreover, using our main result, we derive some others involving systems of variational inequalities. Finally, we give some numerical examples to support our main result.
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Mohammed El Mokhtar Ould El Mokhtar;Saleh Fahad Aljurbua 419
This paper is devoted to the existence of solutions for Kirchhoff type equations with singular nonlinearities, sub-critical and critical exponent. By using the Nehari manifold and Maximum principle theorem, the existence of at least two distinct positive solutions is obtained. -
Mohammed B. M. Altalla;B. Shanmukha;Ahmad El-Ajou;Mohammed N. A. Alkord 435
This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations. -
Reingachan N;Mayanglambam Singhajit Singh;Nirmal Kumar Singha;Khangembam Babina Devi;Barchand Chanam 451
If a0 + Σnν=μ aνzν, 1 ≤ µ ≤ n, is a polynomial of degree n having no zeroin |z| < k, k ≥ 1 and p'(z) its derivative, then Qazi [19] proved$$\max_{{\left|z\right|=1}}\left|p\prime(z)\right|\leq{n}\frac{1+\frac{{\mu}}{n}\left|\frac{a_{\mu}}{a_0} \right|k^{{\mu}+1}}{1+k^{{\mu}+1}+\frac{{\mu}}{n}\left|\frac{a_{\mu}}{a_0} \right|(k^{{\mu}+1}+k^{2{\mu}})}\max_{{\left|z\right|=1}}\left|p(z)\right|$$ In this paper, we not only obtain the Lr version of the polar derivative of the above inequality for r > 0, but also obtain an improved Lr extension in polar derivative. -
The concept of an extension α-F-contraction and it's modified counterpart represents an advancement in the theory of metric space contractions. Through our study of the contraction principles and it's relationship to extension and modified extension, we found different conditions somewhat lengthy. In our paper, we create a development of the conditions for the extension of α-F-contraction and a modified α-F-contraction by reducing the conditions and make them easier. Our propose conditions are notably simple and effective. They serve as the foundation for proving theorems and solving examples that belong to our study. Moreover, they have remarkable significance in the condition of mathematical analysis and problem-solving. Thus, we find that these new conditions that we mention in the definitions achieve what is require and through them, we choose λ = 1 and we choose λ ∈ (0, 1) to clarify our ideas.
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Youssef Achtoun;Mohammed Sefian Lamarti;Ismail Tahiri 477
In this work, we will generalize the notion of multivalued (ν, 𝒞)-contraction mapping in 𝑏-Menger spaces and we shall give a new fixed point result of this type of mappings. As a consequence of our main result, we obtained the corresponding fixed point theorem in fuzzy 𝑏-metric spaces. Also, an example will be given to illustrate the main theorem in ordinary 𝑏-metric spaces. -
The main motivation for this paper is to investigate the fixed point property for nonlinear contraction defined on b-Menger inner product spaces. First, we introduce a b-Menger inner product spaces, then the topological structure is discussed and the probabilistic Pythagorean theorem is given and established. Also we prove the existence and uniqueness of fixed point in these spaces. This result generalizes and improves many previously known results.
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Ali Abd Alaziz Najem Al-Sudani;Ibrahem Abdulrasool hammood Al-Nuh 501
The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results. -
In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.
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Shahd H. Alkharaz;Essam El-Siedy;Eliwa M. Roushdy;Muner M. Abou Hasan 527
In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation. -
In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.
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H. K. Nashine;G. S. Saluja;G. V. V. Jagannadha Rao;W. H. Lim 559
In this paper, we aim to prove coupled and common coupled fixed point theorems for contractive type conditions in the context of partial metric spaces by means of a control function, and to provide some corollaries of the established results. This paper presents a number of results that generalize and extend previous work in the field. In order to better illustrate the process, we provide examples. -
Khairul Habib Alam;Yumnam Rohen;S. Surendra Singh;Kshetrimayum Mangijaobi Devi;L. Bishwakumar 581
A new variety of non-self generalized proximal contraction, called Hardy-Rogers α+F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α+F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation. -
In this study, the conformable fractional derivative(CFD) of order 𝝔 in conjunction with the LC operator of orderρ is used to develop the model of the transmission of the A(H1N1) influenza infection. A brand-new A(H1N1) influenza infection model is presented, with a population split into four different compartments. Fixed point theorems were used to prove the existence of the solutions and uniqueness of this model. The basic reproduction number R0 was determined. The least and most sensitive variables that could alter R0 were then determined using normalized forward sensitivity indices. Through numerical simulations carried out with the aid of the Adams-Moulton approach, the study also investigated the effects of numerous biological characteristics on the system. The findings demonstrated that if 𝝔 < 1 and ρ < 1 under the CFD, also the findings demonstrated that if 𝝔 = 1 and ρ = 1 under the CFD, the A(H1N1) influenza infection will not vanish.