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UNIFYING A MULTITUDE OF COMMON FIXED POINT THEOREMS EMPLOYING AN IMPLICIT RELATION
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 Title & Authors
UNIFYING A MULTITUDE OF COMMON FIXED POINT THEOREMS EMPLOYING AN IMPLICIT RELATION
Ali, Javid; Imdad, Mohammad;
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 Abstract
A general common fixed point theorem for two pairs of weakly compatible mappings using an implicit function is proved without any continuity requirement which generalizes the result due to Popa [20, Theorem 3]. In process, several previously known results due to Fisher, Kannan, Jeong and Rhoades, Imdad and Ali, Imdad and Khan, Khan, Shahzad and others are derived as special cases. Some related results and illustrative examples are also discussed. As an application of our main result, we prove an existence theorem for the solution of simultaneous Hammerstein type integral equations.
 Keywords
implicit functions;weakly compatible mappings;coincidence and fixed points;
 Language
English
 Cited by
1.
Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory and Applications, 2012, 2012, 1, 105  crossref(new windwow)
2.
Unified relation-theoretic metrical fixed point theorems under an implicit contractive condition with an application, Fixed Point Theory and Applications, 2016, 2016, 1  crossref(new windwow)
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