Multivalued -weakly Picard mappings

Kamran, Tayyab

doi:10.1016/j.na.2006.09.010

Cited by 29 publications

(32 citation statements)

References 12 publications

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“…Kamran [20] extended the notion of a multivalued weak contraction mapping to a hybrid pair {f, T } of single valued mapping f and multivalued mapping T. For more discussion on multivalued mappings, we refer to [5,6,8,17,18,22] and references therein. Definition 1.8.…”

Section: Definition 16 ([12]mentioning

confidence: 99%

Generalized dynamic process for generalized (f,L)-almost F-contraction with applications

Hussain¹,

Arshad²,

Abbas³

et al. 2016

J. Nonlinear Sci. Appl.

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Recently Abbas [M. Abbas, Fixed Point Theory, 13 (2012), 3-10] introduced the concept of f −almost contraction which in turn extended the class of multivalued almost contraction mapping and obtained coincidence point results for this new class of mappings. The aim of this paper is to introduce the notion of dynamic process for generalized (f, L)− almost F −contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.

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Section: Definition 16 ([12]mentioning

confidence: 99%

Generalized dynamic process for generalized (f,L)-almost F-contraction with applications

Hussain¹,

Arshad²,

Abbas³

et al. 2016

J. Nonlinear Sci. Appl.

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“…Berinde and Berinde [12] introduced the notion of multivalued (θ, L)-weak contraction and generalized multivalued (θ, L)-weak contraction and obtained some fixed point theorems. Kamran [17] further extended the notion of weak contraction mapping which is more general than the contraction mapping and introduced the notion of multi-valued (f, θ, L)-weak contraction mapping and generalized multi-valued (f, α, L)-weak contraction mapping. He established some coincidence and common fixed point theorems.…”

Section: Introductionmentioning

confidence: 99%

“…We state the results of [17] for convenience as follows: Theorem 1.1. Let (X, d) be a metric space, f : X → X and T : X → CB(X) be a multivalued (f, θ, L)-weak contraction such that T X ⊂ f X.…”

Section: Introductionmentioning

confidence: 99%

Multivalued f -weakly Picard mappings on partial metric spaces

Huang¹,

Li²,

Zhu³

2015

J. Nonlinear Sci. Appl.

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“…Then Kikkawa and Suzuki [8] gave another generalization which generalized the work of Suzuki and the Nadler fixed point theorem. Very Recently Bose and Roychowdhury [3] presented a theorem concerning (θ, L) -multivalued weak contraction which generalized the work of Kikkawa and Suzuki, Nadler [10], Kamran [7], and Berinde and Berinde [1]. Also Mot and Petrusel [9] gave another generalization concerning special multivalued generalized contractions which extended the result of Kikkawa and Suzuki.…”

Section: Introductionmentioning

confidence: 99%

Some Suzuki Type Fixed Point Theorems for Generalized Contractive Multifunctions

Bose¹

2013

Int. J. of Pure and Appl. Math.

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The Banach contraction principle plays a very important role in nonlinear analysis and has many genralizations. Recently Suzuki (2008) gave a new generalization. Then, his method was extended by Kikkawa and Suzuki (2008). Then, Mot and Petrusel (2009), Dhompapangasa and Yingtaweesttikulue (2009), Bose and Roychowdhury (2011), Singh and Mishra (2010, and Doric and Lazovic (2011) further extended their work. In this paper, some results (Theorem 3.1 and Theorem 3.4 and their corollaries) in this direction concerning (common) fixed point theorems for generalized contractive multivalued mappings are presented using a result of Bose and Mukherjee(1977) which extend the results obtained by Bose and Mukherjee, Bose and Roychowdhury (with some constraint), Singh and Mishra, Kikkawa and Suzuki, Mot and Petrusel and others. In Theorem 3.7, a coincidence point theorem for a hybrid pair of mappings f : X → X and T : X → CB(X) is presented.

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Multivalued -weakly Picard mappings

Cited by 29 publications

References 12 publications

Generalized dynamic process for generalized (f,L)-almost F-contraction with applications

Generalized dynamic process for generalized (f,L)-almost F-contraction with applications

Multivalued f -weakly Picard mappings on partial metric spaces

Some Suzuki Type Fixed Point Theorems for Generalized Contractive Multifunctions

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