On fixed point theorems for mappings with PPF dependence

Farajzadeh, Ali; Kaewcharoen, Anchalee

doi:10.1186/1029-242x-2014-372

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…Farajzadeh, Kaewcharoen and Plubtieng [14] introduced the concept of PPF dependent fixed points of multi-valued mappings as follows.…”

Section: Preliminariesmentioning

confidence: 99%

“…Definition 9. [14] Let f : E 0 → E 0 be a single-valued mapping and T : E 0 → CB(E) be a multi-valued mapping. A point ϕ ∈ E 0 is said to be a PPF dependent coincidence point of f and T if f ϕ(c) ∈ T ϕ for some c ∈ I.…”

Section: Preliminariesmentioning

confidence: 99%

“…Several mathematicians proved the existence of PPF dependent fixed points of single-valued mapppings and multi-valued mappings, for more details we refer to [2-5, 7,13, 15, 18]. In 2016, Farajzadeh, Kaewcharoen and Plubtieng [14] introduced the concept of PPF dependent fixed point of multi-valued mappings which is an extension of PPF dependent fixed point of single valued mapping and proved the existence of PPF dependent fixed point for multi-valued mappings.…”

Section: Introductionmentioning

confidence: 99%

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PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings

BABU,

VINOD KUMAR

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this paper, we introduce the notion of generalized weakly contractive type multi-valued mapping with respect to a single-valued mapping and prove the existence of PPF dependent coincidence points in Banach spaces. Further, we introduce the notion of generalized weakly contractive type multivalued mappings for a pair of multi-valued mappings and prove the existence of PPF dependent common fixed points in Banach spaces. We draw some corollaries and provide nontrivial examples to illustrate our results.

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“…Farajzadeh, Kaewcharoen and Plubtieng [14] introduced the concept of PPF dependent fixed points of multi-valued mappings as follows.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings

BABU,

VINOD KUMAR

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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PPF Dependent Fixed Points in Razumikhin Metrical Chains

Turinici

2019

Mathematical Analysis and Applications

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The PPF dependent fixed point result in algebraically closed Razumikhin classes due to Agarwal et al [Fixed Point Theory Appl., 2013, 2013 is identical with its constant class counterpart; and this, in turn, is reducible to a fixed point principle involving SVV type contractions (over the subsequent metric space of initial Banach structure), without any regularity conditions about the Razumikhin classes. The conclusion remains valid for all PPF dependent fixed point results founded on such global conditions. 2010 Mathematics Subject Classification. 47H10 (Primary), 54H25 (Secondary).

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PPF-Dependent Fixed Point Results for New Multi-Valued Generalized F-Contraction in the Razumikhin Class with an Application

Hammad

Sen

2019

Mathematics

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In this paper, a new multi-valued generalized F-contraction mapping is given. Using it, the existence of PPF-dependent fixed point for such mappings in the Razumikhin class is obtained. Moreover, an application for nonlinear integral equations with delay is presented here to illustrate the usability of the obtained results.Definition 1 ([10]). A nonlinear self-mapping T on a metric space (X, d) is said to be an F-contraction, if there exist F ∈ Γ and τ ∈ (0, +∞) such that d(Tx, Ty) > 0 ⇒ τ + F(d(Tx, Ty)) ≤ F(d(x, y)) ∀x, y ∈ X.(1)where Γ is the set of functions F : (0, +∞) → R such that the following axioms hold: (F 1 ) F is strictly increasing, i.e., for all a, b ∈ R + such that a < b, F(a) < F(b); (F 2 ) for every sequence {a n } n∈N of positive numbers lim n→∞ a n = 0 iff lim n→∞ F(a n ) = −∞;The following functions F i : (0, +∞) −→ R for i ∈ {1, 2, 3, 4}, are all the elements of Γ. Furthermore, substituting in Condition (1) these functions, we obtain the following contractions known in the literature, for all x, y ∈ X with α > 0 and Tx = Ty,From the axiom (F 1 ) and Condition (1), one can conclude that every F-contraction T is a contractive mapping and hence automatically continuous.Hence, T is a contraction with a constant 1 2 . Let ξ(t) = t 2 + 1 for all t ∈ [0, 1]. Since T(ξ) = 1 2 sup t∈[0,1] |ξ(t)| = 1 = ξ(0), we have: ξ is a PPF fixed point with dependence of T. Definition 4 ([1]). Let T, S : E • → E be two operators. A point ξ ∈ E • is called a PPF-dependent common fixed point or a common fixed point with PPF-dependentence of T and S if T(ξ) = S(ξ) = ξ(c) for some c ∈ I.Clearly, if we take T = S, then a PPF-dependent common fixed point of T and S collapses to a PPF-dependent fixed point.Definition 5 ([26]). Let P : E • → E and Q : E • → E • . A point ξ ∈ E • is called a PPF-dependent coincidence point or coincidence point with PPF-dependentence of P and Q if P(ξ) = Q(ξ)(c) for some c ∈ I.Let CB(E) be a collection of all non-empty closed bounded subsets of E, and H be the Hausdorff metric determined by . E . Then, for all G, V ∈ CB(E),In 1989, Mizoguchi and Takahashi [27] extended Banach fixed point theorem in a complete metric space. After that, Farajzadeh et al. [28] extended the above results by introducing the following definitions:Please note that if S : E 0 → E is a single-valued mapping, then a multivalued mapping T : E • → CB(E) can be obtained by T(ξ) = {S(ξ)}, for all ξ ∈ E • . Hence, the set of PPF-dependent fixed points of S coincides with the set of PPF-dependent fixed point of T.

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On fixed point theorems for mappings with PPF dependence

Cited by 3 publications

References 8 publications

PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings

PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings

PPF Dependent Fixed Points in Razumikhin Metrical Chains

PPF-Dependent Fixed Point Results for New Multi-Valued Generalized F-Contraction in the Razumikhin Class with an Application

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