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COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS IN S-METRIC SPACES
Javaheri Atena,Sedghi Shaban,Hyun Ho Geun 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.2
In this paper, we present some definitions of S-metric spaces and prove a common fixed point theorem for two mappings under the condition of weakly compatible mappings in complete S-metric spaces. Also we improved some fixed point theorems in complete S-metric spaces.
TRIGONOMETRIC JACKSON INTEGRALS APPROXIMATION BY A k-GENERALIZED MODULUS OF SMOOTHNESS
Hawraa Abbas Almurieb,Zainab Abdulmunim Sharba,Mayada Ali Kareem 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
The need for smoothness measures emerged by mathematicians working in the fields of approximation theory, functional analysis and real analysis. In the present paper, anew version of generalized modulus of smoothness is studied. The aim of defining that modulus,is to find the degree of best Lp functions approximation via trigonometric polynomials.We benefit from Jackson integrals to arrive to the essential approximation theorems
INVERSE PROBLEM FOR STOCHASTIC DIFFERENTIAL EQUATIONS ON HILBERT SPACES DRIVEN BY LÉVY PROCESSES
N. U. Ahmed 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
In this paper we consider inverse problem for a general class of nonlinear stochastic dierential equations on Hilbert spaces whose generating operators (drift, diusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diusion and jump kernel).
ERGODIC SHADOWING, ḏ-SHADOWING AND EVENTUAL SHADOWING IN TOPOLOGICAL SPACES
Sonika Akoijam,Khundrakpam Binod Mangang 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
We define the notions of ergodic shadowing property, ḏ-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, ḏ-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.
AN EFFICIENT THIRD ORDER MANN-LIKE FIXED POINT SCHEME
Pravin Singh,Virath Singh,Shivani Singh 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore,we prove that this scheme is equivalent to the Mann iterative scheme. A comparisonis made with the other third order iterative methods. Results are presented in a table to support our conclusion.
Ahmed A.H. Alkhalidi,Hai a Muhsan B. Alrikabi,Mujtaba Zuhair Ali 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
This study finds three different solutions (3-Sol's) for the fourth order nonlinear discrete anisotropic equations (DAE) with real parameter. We use the variational method(VM) and ϕp-Laplacian operator (ϕp-LO) to prove the main results. In the following paper, we take the parameters λ, μ such that λ>0 and μ≥0 into consideration.
GENERALIZED α-NONEXPANSIVE MAPPINGS IN HYPERBOLIC SPACES
Jong Kyu Kim,Samir Dashputre,Padmavati,Kavita Sakure 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.3
This paper deals with the new iterative algorithm for approximating the fixed point of generalized α-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized α-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.
Le Thi Phuong Ngoc,Nguyen Vu Dzung,Nguyen Thanh Long 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.3
In this paper, we study a system of nonlinear wave equations associated withthe helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.
CONVERGENCE THEOREMS FOR TWO NONLINEAR MAPPINGS IN CAT(0) SPACES
Kritsana Sokhuma,Kasinee Sokhuma 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.3
In this paper, we construct an iteration scheme involving a hybrid pair of the Suzuki generalized nonexpansive single-valued and multi-valued mappings in a complete CAT(0) space. In process, we remove a restricted condition (called end-point condition) in Akkasriworn and Sokhuma's results [2] in Banach spaces and utilize the same to prove some convergence theorems. The results in this paper, are analogs of the results of Akkasriwornet al. [3] in Banach spaces.
Gue Myung Lee,Jae Hyoung Lee 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
In this paper, we consider matrix optimization problems. We investigate augmented Lagrangian methods of multipliers and alternating direction methods of multipliersfor the problems. Following the proofs of Eckstein [3], and Eckstein and Yao [5], we proveconvergence theorems for augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems.