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An iterative method for common solution to various problems
IBRAHIM KARAHAN,SAFEER HUSAIN KHAN 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.3
In this paper, we introduce a new iterative method to nd a common solution of a generalized mixed equilibrium problem, a vari- ational inequality problem and a hierarchical xed point problem for demicontinuous nearly nonexpansive mappings. We prove that our method converges strongly to a common solution of all above problems. It is worth noting that Main Theorem is proved without usual demiclosed- ness condition. As our iterative method generalizes several methods, the results here improve and extend many recent results.
APPROXIMATING FIXED POINTS OF NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES WITHOUT UNIFORM CONVEXITY
Sahu, Daya Ram,Khan, Abdul Rahim,Kang, Shin Min Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.
Approximating fixed points of nonexpansive type mappings in Banach spaces without uniform convexity
Daya Ram Sahu,강신민,Abdul Rahim Khan 대한수학회 2013 대한수학회보 Vol.50 No.3
Approximate fixed point property problem for Mann itera- tion sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpan- sive mappings on an arbitrary normed space. Our results generalize and extend several known results.
Jong Kyu Kim,Ramesh Prasad Pathak,Samir Dashputre,Shailesh Dhar Diwan,Rajlaxmi Gupta 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.1
In this paper, we study the existence of fixed points, demiclosedness principle and the structure of fixed point sets for the class of nearly asymptotically nonexpansive nonselfmappings in CAT(0) spaces, and also we discuss the strong and triangle-convergence theorems for an iterative scheme introduced by Khan. Our results are improvements of the variouswell-known results of fixed point theory which is established in uniformly convex Banach spaces as well as CAT(0) spaces.