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A unified algorithm for solving split generalized mixed equilibrium problem, and for finding fixed point of nonspreading mapping in Hilbert spaces

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Języki publikacji
EN
Abstrakty
EN
The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.
Wydawca
Rocznik
Strony
211--232
Opis fizyczny
Bibliogr. 44 poz., tab., wykr.
Twórcy
  • School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
  • School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
autor
  • School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
autor
  • School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
Bibliografia
  • [1] Blum E., From optimization and variational inequalities to equilibrium problems, Math. Student, 1994, 63(1-4), 123-145
  • [2] Ceng L.-C., Yao J.-C., A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math., 2008, 214, 186-201
  • [3] Combettes P. L., Hirstoaga S. A., Equilibrium programming in Hilbert space, J. Nonlinear Convex Anal., 2005, 6, 117-136
  • [4] Flam S. D., Antipin A. S., Equilibrium programming using proximal-like algorithm, Math. Programming, 1997, 78(1), Ser. A, 29-41
  • [5] Censor Y., Eflving T., A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 1994, 8, 221-239
  • [6] Censor Y., Bortfeld T., Martin B., Trofimov A., A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 2006, 51(2), 2353-2365
  • [7] Censor Y., Elfving T., Kopf N., Bortfeld T., The multiple-set split feasibility problem and its application for inverse problems, Inverse Problem, 2005, 21(6), 2071-2084
  • [8] Censor Y., Motova A., Segal A., A pertubed projections and subgradient projections for the multiple-set split feasibility problem, J. Math. Anal. Appl., 2007, 327, 1244-1256
  • [9] Chen T., Shen J., Image processing and Analysis variational, PDE, Wavelent and Stochastic Methods, SIAM, Philadelpha, 2005
  • [10] Abass H. A., Ogbuisi F. U., Mewomo O. T., Common solution of split equilibrium problem and fixed point problem with no prior knowledge of operator norm, U.P.B. Sci. Bull., Series A, 2018, 80(1), 175-190
  • [11] Halpern B., Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 1967, 73, 957-961
  • [12] He S., Yeng C., Boundary point algorithms for minimum norm fixed points of nonexpansive mappings, Fixed Point Theory Appl., 2014, 56
  • [13] Jolaoso L. O., Ogbuisi F. U., Mewomo O. T., An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces, Adv. Pure Appl. Math., 2017, DOI: 10.1515/apam-2017-0037
  • [14] Krasnoselskii M. A., Two remarks on the method of successive approximations, Usp. Math. Nauk., 1955, 10, 123-127
  • [15] Mann W. R., Mean value methods in iterations, Proc. Amer. Math. Soc., 1953, 4, 506-510
  • [16] Nakajo K., Takahashi W., Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., 2003, 279(2), 372-379
  • [17] Ogbuisi F. U., Mewomo O. T., Convergence analysis of common solution of certain nonlinear problems, Fixed Point Theory, 2018, 19(1), 335-358
  • [18] Mewomo O. T., Ogbuisi F. U., Convergence analysis of an iterative method for solving multiple-set split feasibility problems in certain Banach spaces, Quest. Math., 2018, 14(1), 129-148
  • [19] Ogbuisi F. U., Mewomo O. T., Iterative solution of split variational inclusion problem in a real Banach space, Afr. Mat., 2017, 28(1-2), 295-309
  • [20] Ogbuisi F. U., Mewomo O. T., On split generalized mixed equilibrium problems and fixed point problems with no prior knowledge of operator norm, J. Fixed Point Theory Appl., 2016, 19(3), 2109-2128
  • [21] Okeke C. C., Mewomo O. T., On split equilibrim problem, variational inequality problem and fixed point problem for multivalued mappings, Ann. Acad. Rom. Sci. Ser. Math. Appl., 2017, 9(2), 255-280
  • [22] Shehu Y., Mewomo O. T., Further investigation into split common fixed point problem for demicontractive operators, Acta Math. Sin. (Engl. Ser.), 2016, 32(11), 1357-1376
  • [23] Shehu Y., Mewomo O. T., Ogbuisi F. U., Further investigation into approximation of a common solution of fixed point problems and split feasibility problems, Acta Math. Sci. Ser. B (Engl. Ed.), 2016, 36(3), 913-930
  • [24] Moudafi A., Viscosity approximation method for fixed-points problems, J. Math. Anal. Appl., 2000, 241(1), 46-55
  • [25] Xu H. K., Viscosity approximation method for nonexpansive mappings, J. Math. Anal. Appl., 2004, 298(1), 279-291
  • [26] Polyak B. T., Some methods of speeding up the convergence of iteration methods, U.S.S.R. Comput. Math. Math. Phys., 1964, 4(5), 1-17
  • [27] Alvarez F., Attouch H., An inertial proximal method for monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Anal., 2001, 9(1-2), 3-11
  • [28] Moudafi A., Oliny M., Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math., 2003, 155(2), 447-454
  • [29] Lorenz D., Pock T., An inertial forward-backward algorithm for monotone inclusions, J. Math. Imaging Vision, 2015, 51(2), 311-325
  • [30] Chen C., Chan R. H., Ma S., Yang J., Inertial proximal ADMM for linearly constrained separable convex optimization, SIAM J. Imaging Sci., 2015, 8(4), 2239-2267
  • [31] Beck A., Teboulle M., A fast iterative shrinkage-thresholding algorithm for linear inverse problem, SIAM J. Imaging Sci., 2009, 2(1), 183-202
  • [32] Chambole A., Dossal C. H., On the convergence of the iterates of the "fast shrinkage/thresholding algorithm", J. Optim. Theory Appl., 2015, 166(3), 968-982
  • [33] Mainge P. E., Convergence theorems for inertial KM-type algorithms, J. Comput. Appl. Math., 2008, 219(1), 223-236
  • [34] Bot R. I., Csetnek E. R., Hendrich C., Inertial Douglas-Rachford splitting for monotone inclusions, Appl. Math. Comput., 2015, 256, 472-487
  • [35] Picard E., Memoire sur la theorie des equations aux derives partielles et la methode des approximation successive, J. Math. Pures et Appl., 1890, 6, 145-210
  • [36] Nocedal J., Wright S. J., Numerical Optimization, Spinger Series in Operations Research and Financial Engineering, Vol 2, 2nd Edition, Spinger, Berlin, 2006
  • [37] Dong Q. L., Yuan H. B., Accelerated Mann and CQ algorithms for finding a fixed point of nonexpansive mapping, Fixed Point Theory Appl., 2015, 2015:125
  • [38] Suntai S., Cholamjiak P., Cho Y. J., Cholamjiak W., On solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert space, Fixed Point Theory Appl., 2016, 2016:35
  • [39] Rizvi S. H., A strong convergence theorem for split mixed equilibrium and fixed point problems for nonexpansive mappings in Hilbert space, J. Fixed Point Thoery Appl., 2018, 20(8), DOI: 10.1007/s11784-018-0487-8
  • [40] Hendrickx J. M., Olshevsky A., Matrix P-norms are NP-hard to approximate if p≠1,2,∞, SIAM J. Matrix Anal. Appl., 2012, 31, 2802-2812
  • [41] Hussain N., Marino G., Abdou A. N., On Mann’s method with viscosity for nonexpansive and nonspreading mapping in Hilbert spaces, Abstr. Appl. Anal., 2014, Article ID: 152530, DOI: 10.1155/2014/152530
  • [42] Li S., Li L., Cao L., He X., Yue X., Hybrid extragradient method for generalized mixed equilibrium problem and fixed point problems in Hilbert space, Fixed Point Theory Appl., 2013, 2013:240
  • [43] Xu H. K., Another control condition in an iterative method for nonexpansive mappings, Bull. Aust. Math. Soc., 2002, 65(1), 109-113
  • [44] Onjai-uea N., Phuengrattana W., On solving split mixed equilibrium problems and fixed point problems of hybrid-type multivalued mappings in Hilbert spaces, J. Ineq. Appl., 2017, 2017:137
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0a235c9a-fd8a-4911-91b9-2554583e505c
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