Common fixed point theorems for hybrid F -contractions and applications
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"Common fixed point theorems for hyb..." refers methods in this paper
...The development of geometric fixed point theory for multivalued mappings was initiated with the work of Nadler, Jr. [28] in the year 1969....
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...Then, on the lines of Nadler [28], we adopt that: (1) CL(X) = {A : A is a non-empty closed subset of X}, (2) CB(X) = {A : A is a non-empty closed and bounded subset of X}, (3) For non-empty closed and bounded subsets A,B of X and x ∈ X, d(x,A) = inf{d(x, a) : a ∈ A}...
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...Then, on the lines of Nadler [28], we adopt that: (1) CL(X) = {A : A is a non-empty closed subset of X}, (2) CB(X) = {A : A is a non-empty closed and bounded subset of X}, (3) For non-empty closed and bounded subsets A,B of X and x ∈ X, d(x,A) = inf{d(x, a) : a ∈ A} and H(A,B) = max {sup{d(a,B) : a ∈ A}, sup{d(b, A) : b ∈ B}} ....
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661 citations
"Common fixed point theorems for hyb..." refers background or methods in this paper
...multivalued F -contractions were obtained in [3, 23, 47], resp....
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...A)); (iii) any requirement of closedness of the range of f is relaxed; (iv) a new kind of contractive conditions (so-called F -contraction conditions) are used, that originated in the work of Wardowski [47]....
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...Some examples of functions F ∈ F are F (t) = ln t, F (t) = t + ln t, F (t) = −1/ √ t, see [47]....
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...[47] Let F : R → R be given by F (x) = lnx....
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...coincidentally idempotent mappings satisfying closed multi-valued F -contraction condition introduced by Wardowski [Fixed Point Theory Appl....
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547 citations
"Common fixed point theorems for hyb..." refers background in this paper
...A) (previously introduced for singlevalued mappings by Aamri and Moutawakil [1]) to hybrid pairs of mappings....
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406 citations