APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

doi:10.1007/s10473-019-0203-9

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 369-381.doi: 10.1007/s10473-019-0203-9

APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

Iz-iddine EL-FASSI¹, Hamid KHODAEI², Themistocles M. RASSIAS³

1. Department of Mathematics, Faculty of Sciences, Ibn Tofaïl University, B. P. 133, Kenitra, Morocco;
2. Department of Mathematics, Malayer University, P. O. Box 65719-95863, Malayer, Iran;
3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

收稿日期:2018-04-11 修回日期:2018-06-17 出版日期:2019-04-25 发布日期:2019-05-06
通讯作者: Iz-iddine EL-FASSI E-mail:izidd-math@hotmail.fr;izelfassi.math@gmail.com
作者简介:Hamid KHODAEI,hkhodaei.math@gmail.com;Themistocles M. RASSIAS,trassias@math.ntua.gr

APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

Iz-iddine EL-FASSI¹, Hamid KHODAEI², Themistocles M. RASSIAS³

1. Department of Mathematics, Faculty of Sciences, Ibn Tofaïl University, B. P. 133, Kenitra, Morocco;
2. Department of Mathematics, Malayer University, P. O. Box 65719-95863, Malayer, Iran;
3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

Received:2018-04-11 Revised:2018-06-17 Online:2019-04-25 Published:2019-05-06
Contact: Iz-iddine EL-FASSI E-mail:izidd-math@hotmail.fr;izelfassi.math@gmail.com

摘要/Abstract

摘要： In this paper, using the Brzd?k’s fixed point theorem [9, Theorem 1] in non-Archimedean (2, β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation

where p ∈ {1, …, 5}, a₁, …, a_k are fixed nonzero reals when p ∈ {1, 3, 5} and are fixed positive reals when p ∈ {2, 4}.

关键词: fixed point theorem, p-th root functional equation, stability, non-Archimedean (2,β)-normed spaces

Abstract: In this paper, using the Brzd?k’s fixed point theorem [9, Theorem 1] in non-Archimedean (2, β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation

where p ∈ {1, …, 5}, a₁, …, a_k are fixed nonzero reals when p ∈ {1, 3, 5} and are fixed positive reals when p ∈ {2, 4}.

Key words: fixed point theorem, p-th root functional equation, stability, non-Archimedean (2,β)-normed spaces

Iz-iddine EL-FASSI, Hamid KHODAEI, Themistocles M. RASSIAS. APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES[J]. 数学物理学报(英文版), 2019, 39(2): 369-381.

Iz-iddine EL-FASSI, Hamid KHODAEI, Themistocles M. RASSIAS. APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES[J]. Acta mathematica scientia,Series B, 2019, 39(2): 369-381.

参考文献

[1] Agarwal R P, Xu B, Zhang W. Stability of functional equations in single variable. J Math Anal Appl, 2003, 288:852-869
[2] Aiemsomboon L, Sintunavarat W. On a new type of stability of a radical quadratic functional equation using Brzdęk's fixed point theorem. Acta Math Hungar, 2017, 151(1):35-46
[3] Alizadeh Z, Ghazanfari A G. On the stability of a radical cubic functional equation in quasi-β-spaces. J Fixed Point Theory Appl, 2016, 18:843-853
[4] Aoki T. On the stability of the linear transformation in Banach spaces. J Math Soc Japan, 1950, 2:64-66
[5] Bourgin D G. Approximately isometric and multiplicative transformations on continuous function rings. Duke Math J, 1949, 16:385-397
[6] Bourgin D G. Classes of transformations and bordering transformations. Bull Amer Math Soc, 1951, 57:223-237
[7] Brzdęk J. Hyperstability of the Cauchy equation on restricted domains. Acta Math Hungar, 2013, 141(1/2):58-67
[8] Brzdęk J. Remarks on solutions to the functional equations of the radical type. Adv Theory Nonlinear Anal Appl, 2017, 1(2):125-135
[9] Brzdęk J, Ciepliński K. A fixed point approach to the stability of functional equations in non-Archimedean metric spaces. Nonlinear Anal, 2011, 74:6861-6867
[10] Brzdęk J, Ciepliński K. Hyperstability and superstability. Abstr Appl Anal, 2003, 2013:Article ID 401756
[11] Brzdęk J, Ciepliński K. On a fixed point theorem in 2-Banach spaces and some of its applications. Acta Math Sci, 2018, 38B(2):377-390
[12] Brzdęk J, Fechner W, Moslehian M S, Sikorska J. Recent developments of the conditional stability of the homomorphism equation. Banach J Math Anal, 2015, 9:278-327
[13] Dung N V, Hang V T L. The generalized hyperstability of general linear equations in quasi-Banach spaces. J Math Anal Appl, 2018, 462:131-147
[14] EL-Fassi Iz. On a new type of hyperstability for radical cubic functional equation in non-Archimedean metric spaces. Results Math, 2017, 72:991-1005
[15] EL-Fassi Iz. Approximate solution of radical quartic functional equation related to additive mapping in 2-Banach spaces. J Math Anal Appl, 2017, 455:2001-2013
[16] EL-Fassi Iz. A new type of approximation for the radical quintic functional equation in non-Archimedean (2, β)-Banach spaces. J Math Anal Appl, 2018, 457:322-335
[17] EL-Fassi Iz. On the general solution and hyperstability of the general radical quintic functional equation in quasi-β-Banach spaces. J Math Anal Appl, 2018, 466:733-748
[18] EL-Fassi Iz. Solution and approximation of radical quintic functional equation related to quintic mapping in quasi-β-Banach spaces. RACSAM, 2018, https://doi.org/10.1007/s13398-018-0506-z
[19] EL-Fassi Iz, Brzdęk J, Chahbi A, Kabbaj S. On hyperstability of the biadditive functional equation. Acta Math Sci, 2017, 37B(6):1727-1739
[20] El-Fassi Iz, Kabbaj S. On the generalized orthogonal stability of the Pexiderized quadratic functional equation in modular space. Math Slovaca, 2017, 67(1):165-178
[21] Gähler S. Lineare 2-normierte Räume. Math Nachr, 1964, 28:1-43(in German)
[22] Gähler S. Über 2-Banach-Räume. Math Nachr, 1969, 42:335-347(in German)
[23] Gajda Z. On stability of additive mappings. Int J Math Math Sci, 1991, 14:431-434
[24] Găvruta P. A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J Math Anal Appl, 1994, 184:431-436
[25] Gordji M E, Khodaei H, Rassias Th M. A Functional Equation Having Monomials and Its Stability. Optimization and Its Applications, 96. Springer, 2014
[26] Hensel K. Über eine neue Begründung der Theorie der algebraischen Zahlen. Jahresber Dtsch Math-Ver, 1897, 6:83-88
[27] Hyers D H. On the stability of the linear functional equation. Proc Nat Acad Sci, USA, 1941, 27:222-224
[28] Katsaras A K, Beoyiannis A. Tensor products of non-Archimedean weighted spaces of continuous functions. Georgian Math J, 1999, 6:33-44
[29] Khodaei H, Eshaghi Gordji M, Kim S S, Cho Y J. Approximation of radical functional equations related to quadratic and quartic mappings. J Math Anal Appl, 2012, 395:284-297
[30] Khrennikov A. Non-Archimedean Analysis:Quantum Paradoxes, Dynamical Systems and Biological Models. Mathematics and Its Applications, 427. Dordrecht:Kluwer Academic, 1997
[31] Maksa G, Páles Z. Hyperstability of a class of linear functional equations. Acta Math Acad Paedagog Nyháazi (NS), 2001, 17:107-112
[32] Moslehian M S, Rassias Th M. Stability of functional equations in non-Archimedean spaces. Appl Anal Discrete Math, 2007, 1:325-334
[33] Nyikos P J. On some non-Archimedean spaces of Alexandrof and Urysohn. Topol Appl, 1999, 91:1-23
[34] Rassias Th M. On the stability of the linear mapping in Banach spaces. Proc Amer Math Soc, 1978, 72:297-300
[35] Rassias Th M. On a modified Hyers-Ulam sequence. J Math Anal Appl, 1991, 158:106-113
[36] Rassias Th M, Semrl P. On the behavior of mappings which do not satisfy Hyers-Ulam stability. Proc Amer Math Soc, 1992, 114:989-993
[37] Ulam S M. A Collection of Mathematical Problems. New York:Interscience Publishers, 1960; Reprinted as:Problems in Modern Mathematics. New York:John Wiley & Sons, Inc, 1964
[38] White A. 2-Banach spaces. Math Nachr, 1969, 42:43-60
[39] Xu B, Brzdęk J, Zhang W. Fixed point results and the Hyers-Ulam stability of linear equations of higher orders. Pacific J Math, 2015, 273(2):483-498

APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 6

[1]	梁载涛, 杨艳娟. RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE[J]. 数学物理学报(英文版), 2019, 39(2): 395-402.
[2]	Muaadh ALMAHALEBI, Abdellatif CHAHBI. APPROXIMATE SOLUTION OF P-RADICAL FUNCTIONAL EQUATION IN 2-BANACH SPACES[J]. 数学物理学报(英文版), 2019, 39(2): 551-566.
[3]	刘春根, 张晓飞. STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH[J]. 数学物理学报(英文版), 2019, 39(1): 111-126.
[4]	潘洁, 方莉, 郭真华. STABILITY OF BOUNDARY LAYER TO AN OUTFLOW PROBLEM FOR A COMPRESSIBLE NON-NEWTONIAN FLUID IN THE HALF SPACE[J]. 数学物理学报(英文版), 2019, 39(1): 259-283.
[5]	张海湘, 杨雪花, 徐大. ALTERNATING DIRECTION IMPLICIT OSC SCHEME FOR THE TWO-DIMENSIONAL FRACTIONAL EVOLUTION EQUATION WITH A WEAKLY SINGULAR KERNEL[J]. 数学物理学报(英文版), 2018, 38(6): 1689-1711.
[6]	刘丽雅, 蒋达清, Tasawar HAYAT, Bashir AHMAD. DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE[J]. 数学物理学报(英文版), 2018, 38(6): 1731-1750.
[7]	薛焕斌, 张继业. ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING[J]. 数学物理学报(英文版), 2018, 38(6): 1921-1938.
[8]	陈贵强, Matthew RIGBY. STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW[J]. 数学物理学报(英文版), 2018, 38(5): 1485-1514.
[9]	唐少君, 张澜. NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION[J]. 数学物理学报(英文版), 2018, 38(3): 973-1000.
[10]	周永辉, 杨赟瑞, 刘克盼. STABILITY OF TRAVELING WAVES IN A POPULATION DYNAMIC MODEL WITH DELAY AND QUIESCENT STAGE[J]. 数学物理学报(英文版), 2018, 38(3): 1001-1024.
[11]	Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 377-390.
[12]	P. BASKAR, S. PADMANABHAN, M. SYED ALI. FINITE-TIME H_∞ CONTROL FOR A CLASS OF MARKOVIAN JUMPING NEURAL NETWORKS WITH DISTRIBUTED TIME VARYING DELAYS-LMI APPROACH[J]. 数学物理学报(英文版), 2018, 38(2): 561-579.
[13]	A. M. NAGY, N. H. SWEILAM. NUMERICAL SIMULATIONS FOR A VARIABLE ORDER FRACTIONAL CABLE EQUATION[J]. 数学物理学报(英文版), 2018, 38(2): 580-590.
[14]	Rakesh KUMAR, Anuj Kumar SHARMA, Kulbhushan AGNIHOTRI. STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL[J]. 数学物理学报(英文版), 2018, 38(2): 709-732.
[15]	宋威, 李林. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION[J]. 数学物理学报(英文版), 2018, 38(1): 177-186.