BEST PROXIMITY POINT THEOREMS IN HADAMARD SPACES USING RELATIVELY ASYMPTOTIC CENTER

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GABELEH M.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2017 | Volume:2 | Issue:8 Page(s): 45-58

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Title

BEST PROXIMITY POINT THEOREMS IN HADAMARD SPACES USING RELATIVELY ASYMPTOTIC CENTER

Author(s)

GABELEH M. | Issue Writer Certificate

Keywords

BEST PROXIMITY POINTQ1

RELATIVELY ASYMPTOTIC CENTERQ1

HADAMARD METRIC SPACEQ1

NONEXPANSIVE NON-SELF MAPPINGQ1

Abstract

In this article we survey the existence of BEST PROXIMITY POINTs for a class of non-self mappings which satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [A. Abkar, M. Gabeleh, BEST PROXIMITY POINTs of non-self mappings, Top, 21, (2013), 287-295] which guarantees the existence of BEST PROXIMITY POINTs for NONEXPANSIVE NON-SELF MAPPINGs in the setting of uniformly convex Banach spaces.We also introduce a new notion, called RELATIVELY ASYMPTOTIC CENTER, on a nonempty, bounded, closed and convex pair of subsets of a HADAMARD METRIC SPACE and as a result of our main conclusions, we will show that the asymptotic center of any sequence in a nonempty, bounded, closed and convex subset of a Hadamard space is singleton. Moreover, we obtain the other existence results of BEST PROXIMITY POINTs for generalized nonexpansive mappings using the appropriate geometric properties of Hadamard spaces. Finally, we provide some examples to illustrate our main results.

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APA: Copy

GABELEH, M.. (2017). BEST PROXIMITY POINT THEOREMS IN HADAMARD SPACES USING RELATIVELY ASYMPTOTIC CENTER. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 2(8), 45-58. SID. https://sid.ir/paper/257279/en

Vancouver: Copy

GABELEH M.. BEST PROXIMITY POINT THEOREMS IN HADAMARD SPACES USING RELATIVELY ASYMPTOTIC CENTER. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2017;2(8):45-58. Available from: https://sid.ir/paper/257279/en

IEEE: Copy

M. GABELEH, “BEST PROXIMITY POINT THEOREMS IN HADAMARD SPACES USING RELATIVELY ASYMPTOTIC CENTER,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 2, no. 8, pp. 45–58, 2017, [Online]. Available: https://sid.ir/paper/257279/en

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