Meir-Keeler type and Caristi type fixed point theorems | Zendy

Abhijit Pant | Zendy; R. P. Pant | Zendy; Vladimir Rakočević | Zendy

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Meir-Keeler type and Caristi type fixed point theorems

Author(s) -

Abhijit Pant,

R. P. Pant,

Vladimir Rakočević

Publication year - 2019

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm181224037p

Subject(s) - mathematics , type (biology) , fixed point theorem , fixed point , discontinuity (linguistics) , discrete mathematics , pure mathematics , mathematical analysis , biology , ecology

Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.

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