Composite relaxed resolvent operator and Yosida approximation operator for solving a system of Yosida inclusions

• Autorzy: Ahmad, R. , Mishra, V. N. , Ishtyak, M. , Rahaman, M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we first study a composite relaxed resolvent operator and prove some of its properties. After that, we introduce a Yosida approximation operator based on the composite relaxed resolvent operator and demonstrate some properties of the Yosida approximation operator. Finally, we obtain the solution of a system of Yosida inclusions by applying these concepts.We construct a conjoin example in support of many concepts derived in this paper. Our concepts and results are new in the literature and can be used for further research.

Słowa kluczowe

PL

inkluzja; układ; rozwiązanie; Yosida

EN

inclusion; relaxed; system; solution; Yosida

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 2
• Strony: 185--195
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Ahmad, R.

• Aligarh Muslim University, Aligarh 202002, India,

autor

Mishra, V. N.

• Madhya Pradesh 484-887; and L. 1627 Awadh Puri Colony Beniganj, Phase - III, Opposite - Industrial Training Institute (I.T.I.), Ayodhya Main Road Faizabad-224 001, (Uttar Pradesh), India,

autor

Ishtyak, M.

• Aligarh Muslim University, Aligarh 202002, India,

autor

Rahaman, M.

• Aligarh Muslim University, Aligarh 202002, India,

Bibliografia

• [1] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, International Publishing, Leyden, 1976.
• [2] F. E. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces American Mathematical Society, Providence, 1976.
• [3] H.-W. Cao, Sensitivity analysis for a system of generalized nonlinear mixed quasi variational inclusions with H-monotone operators, J. Appl. Math. 2011 (2011), Article ID 921835.
• [4] H.-W. Cao, Yosida approximation equations technique for system of generalized set-valued variational inclusions, J. Inequal. Appl. 2013 (2013), Paper No. 455.
• [5] X. P. Ding, Generalized quasi-variational-like inclusions with nonconvex functionals, Appl. Math. Comput. 122 (2001), no. 3, 267-282.
• [6] Y.-P. Fang and N.-J. Huang, H-monotone operator and resolvent operator technique for variational inclusions, Appl. Math. Comput. 145 (2003), no. 2-3, 795-803.
• [7] P. Hartman and G. Stampacchia, On some non-linear elliptic differential-functional equations, Acta Math. 115 (1966), 271-310.
• [8] A. Hassouni and A. Moudafi, A perturbed algorithm for variational inclusions, J. Math. Anal. Appl. 185 (1994), no. 3, 706-712.
• [9] V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford, 1981.
• [10] H.-Y. Lan, Generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity frameworks, Abstr. Appl. Anal. 2013 (2013), Article ID 157190.
• [11] M. Rahaman, R. Ahmad, M. Dilshad and I. Ahmad, Relaxed η-proximal operator for solving a variational-like inclusion problem, Math. Model. Anal. 20 (2015), no. 6, 819-835.
• [12] G. Stampacchia, Formes bilinéaires coercitives sur les ensembles convexes, C. R. Acad. Sci. Paris 258 (1964), 4413-4416.
• [13] R. U. Verma, A-monotonicity and applications to nonlinear variational inclusion problems, J. Appl. Math. Stoch. Anal. 2004 (2004), no. 2, 193-195.
• [14] R. U. Verma, General nonlinear variational inclusion problems involving A-monotone mappings, Appl. Math. Lett. 19 (2006), no. 9, 960-963.
• [15] R. U. Verma, Hybrid inexact proximal point algorithms based on RMM frameworks with applications to variational inclusion problems, J. Appl. Math. Comput. 39 (2012), no. 1-2, 345-365.
• [16] J. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities, J. Math. Anal. Appl. 132 (1988), no. 1, 213-225.

Identyfikatory

DOI

10.1515/jaa-2018-0018