Authors:Sylvain Koumla, Nelio N’Dogotar, Boubacar Diao Abstract: The aim of this work is to prove some results about the existence and regularity of solutions for some neutral partial functional integrodifferential equations with infinite delay in Banach spaces. The results are based on semigroup theory and on Banach’s fixed point theorems. The method used treats the equations in its subspace D(A). One example is given to illustrate the theory. PubDate: 2022-04-18 Issue No:Vol. 12 (2022)
Authors:Narinder Kumar, Manoj Kumar, Ashish - Abstract: In this paper, with the aid of simulation mapping ðœ‚: [0,∞) × [0,∞)->ℝ, we prove some Lemmas and fixed point result for generalized ð’µ − contraction of the mapping ð‘”: ð‘‹->ð‘‹ satisfying the following conditions: ðœ‚(ð’¢(ð‘”ð‘¥, ð‘”ð‘¦, ð‘”ð‘§),ℳ(ð‘¥, ð‘¦, ð‘§)) ≥ 0, for all ð‘¥, ð‘¦, 𑧠∈ ð‘‹, where ℳ(ð‘¥, ð‘¦, ð‘§) = max {ð’¢(ð‘¥, ð‘”ð‘¦, ð‘”ð‘¦), ð’¢(ð‘¦, ð‘”ð‘¥, ð‘”ð‘¥), ð’¢(ð‘¦, ð‘”ð‘§, ð‘”ð‘§), ð’¢(ð‘§, ð‘”ð‘¦, ð‘”ð‘¦), ð’¢(ð‘§, ð‘”ð‘¥, ð‘”ð‘¥), ð’¢(ð‘¥, ð‘”ð‘§, ð‘”ð‘§)}. and (ð‘‹, ð’¢) is a ð’¢ − metric space. An example is also given to support our results. PubDate: 2022-03-30 Issue No:Vol. 12 (2022)
Authors:J. N. Ezeora, F. E. Bazuaye Abstract: In this paper, we propose and study an inexact generalized proximal point algorithm with alternated inertial steps for solving monotone inclusion problem and obtain weak convergence results under some mild conditions. In the case when the operator T is such that T-1 is Lipschitz continuous at 0, we prove that the sequence of the iterates is linearly convergent. Fejer monotonicity of even subsequences of the iterates is also obtained. Finally, we give some priori and posteriori error estimates of our generated sequences. PubDate: 2022-03-30 Issue No:Vol. 12 (2022)
Authors:S. A. M. Mohsenialhosseini Abstract: In this paper, we will first introduce the approximate fixed point property and a new class of operators and contraction mapping for a cyclic map T on modular G-metric spaces. Also, we prove two general lemmas regarding approximate fixed Point of cyclic maps on modular G-metric spaces. Using these results we prove several approximate fixed point theorems for a new class of operators and contraction mapping on modular G-metric spaces. PubDate: 2022-03-11 Issue No:Vol. 12 (2022)
Authors:B. Srinuvasa Rao, E. Gouthami, Ch. Maheswari, Mohiddin Shaw Shaik Abstract: In this paper, we establish a coupled coincidence fixed point results for a hybrid pair of single valued and multivalued mappings satisfying generalized contractive conditions, defined on a partially ordered bipolar metric space. Our results unify, generalize and complement several known comparable results from the current literature. An example is given. PubDate: 2022-02-08 Issue No:Vol. 12 (2022)
Authors:Rong-Hua He, Rui-Jiang Bi Abstract: In this paper, we establish a collectively fixed point theorem and an equilibrium existence theorem for generalized games in product locally FC-uniform spaces. As applications, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are derived in product locally FC-uniform spaces. These theorems are new and generalize some known results in the literature. PubDate: 2022-01-06 Issue No:Vol. 12 (2022)
Authors:R. A. Rashwan, Saleh Omran, Asmaa Fangary Abstract: In this paper we introduce some Banach fixed point theorems in operators of Hilbert C∗-modules, based on a definition of valued operator Hilbert C∗-modules normed space. Also We give some examples to clear our definitions. Finally we discuss the existence and uniqueness of the solution of system of operators on Hilbert C∗-modules. PubDate: 2021-12-13 Issue No:Vol. 12 (2021)
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