SOME FIXED POINT THEOREMS FORGENARALIZEDα-β-FG-CONTRACTIONSINb-METRIC SPACES AND CERTAINAPPLICATIONS TO THE INTEGRALEQUATIONS
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Abstract
The purpose of this paper is to introduce a generalized
α
-
β
-
FG
-
contraction and prove some fixed point theorems in
b
-metric spaces.
These theorems are generalizations of some results in literature. An
example is given to illustrate the obtained results and to show that these
results are proper extensions of the existing ones. Then we apply the
obtained theorem to study the existence of solutions of the integral equa-
tion
α
-
β
-
FG
-
contraction and prove some fixed point theorems in
b
-metric spaces.
These theorems are generalizations of some results in literature. An
example is given to illustrate the obtained results and to show that these
results are proper extensions of the existing ones. Then we apply the
obtained theorem to study the existence of solutions of the integral equa-
tion
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